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28. An oil company has two depots, A and B, with capacities of 7000 L and 4000 L, respectively. The company has to supply oil to three petrol pumps, D, E and F, whose requirements are 4500L, 3000L and 3500L, respectively. The distances (in km) between the depots and the petrol pumps are given in the following table:

Distance in (km)
From/To	A	B
D	7	3
E	6	4
F	3	2

Q7. An oil company has two depots, A and B, with capacities of 7000 L and 4000 L, respectively. The company has to supply oil to three petrol pumps, D, E and F, whose requirements are 4500L, 3000L and 3500L, respectively. The distances (in km) between the depots and the petrol pumps are given in the following table:

Distance in (km)
From/To	A	B
D	7	3
E	6	4
F	3	2

Assuming that the transportation cost of 10 litres of oil is ?. 1 per km, how should the delivery be scheduled in order that the transportation cost is minimum? What is the minimum cost?

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Jhulelal Institute of Technology Colleges in India

Contributor-Level 10

Let x and y litres of oil be supplied from A to the petrol pumps, D and E. So, $(7000 - x - y)$ will be supplied from A to petrol pump F.

The requirement at petrol pump D is 4500 L. Since x L are transported from depot A, the remaining (4500 – x) L will be transported from petrol pump B.

Similarly $, (3000 - y) L a n d 3500 - (7000 - x - y) = (x + y - 3500)$ L will be transported from depot B to petrol pumps E and F, respectively.

The given problem can be represented diagrammatically as given below:

$\begin{array}{l} \end{array} x ? 0, y ? 0, a n d (7000 - x - y) ? 0$

$T h e n, x ? 0, y ? 0, a n d x + y ? 7000$

$4500 - x ? 0, 3000 - y ? 0, a n d x + y - 3500 ? 0$

$T h e n, x ? 4500, y ? 3000, a n d x + y ? 3500$

Cost of transporting 10 L of petrol = Rs. 1

Cost of transporting 1 L of petrol = Rs. 1/10

Hence, the total transportation cost is given by,

$\begin{array}{l} z = (7 / 10) x + (6 / 10) y + 3 / 10 (7000 - x - y) + 3 / 10 (4500 - x) + 4 / 10 (3000 - y) + 2 / 10 (x + y - 3500) \end{array}$

$\begin{array}{l} = 0.3 x + 0.1 y + 3950 \end{array}$

The problem can be formulated as given below:

$M i n i m i s e z = 0.3 x + 0.1 y + 3950 \dots \dots \dots . (i)$

Subject to cons

...more

Let x and y litres of oil be supplied from A to the petrol pumps, D and E. So, $(7000 - x - y)$ will be supplied from A to petrol pump F.

The requirement at petrol pump D is 4500 L. Since x L are transported from depot A, the remaining (4500 – x) L will be transported from petrol pump B.

Similarly $, (3000 - y) L a n d 3500 - (7000 - x - y) = (x + y - 3500)$ L will be transported from depot B to petrol pumps E and F, respectively.

The given problem can be represented diagrammatically as given below:

$\begin{array}{l} \end{array} x ? 0, y ? 0, a n d (7000 - x - y) ? 0$

$T h e n, x ? 0, y ? 0, a n d x + y ? 7000$

$4500 - x ? 0, 3000 - y ? 0, a n d x + y - 3500 ? 0$

$T h e n, x ? 4500, y ? 3000, a n d x + y ? 3500$

Cost of transporting 10 L of petrol = Rs. 1

Cost of transporting 1 L of petrol = Rs. 1/10

Hence, the total transportation cost is given by,

$\begin{array}{l} z = (7 / 10) x + (6 / 10) y + 3 / 10 (7000 - x - y) + 3 / 10 (4500 - x) + 4 / 10 (3000 - y) + 2 / 10 (x + y - 3500) \end{array}$

$\begin{array}{l} = 0.3 x + 0.1 y + 3950 \end{array}$

The problem can be formulated as given below:

$M i n i m i s e z = 0.3 x + 0.1 y + 3950 \dots \dots \dots . (i)$

Subject to constraints,

$\begin{array}{l} \end{array} x + y ? 7000 \dots \dots \dots . (i i)$

$x ? 4500 \dots \dots \dots . . (i i i)$

$y ? 3000 \dots \dots . (i v)$

$x + y ? 3500 \dots \dots \dots (v)$

$x, y ? 0 \dots \dots \dots \dots (v i)$

The feasible region determined by the constraints is given below:

A (3500, 0), B (4500, 0), C (4500, 2500), D (4000, 3000) and E (500, 3000) are the corner points of the feasible region.

The values of z at these corner points are given below:

Corner Point	z = 0.3x + 0.1y + 3950
A (3500, 0)	5000
B (4500, 0)	5300
C (4500, 2500)	5550
D (4000, 3000)	5450
E (500, 3000)	4400	Minimum

The minimum value of z is 4400 at (500, 3000).

Hence, the oil supplied from depot A is 500 L, 3000 L and 3500 L, and from depot B is 4000 L, 0 L and 0 L to petrol pumps D, E and F, respectively.

Therefore, the minimum transportation cost is ?. 4400.

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11 months ago

How many companies were a part of Jhulelal Institute of Technology placements?

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Jhulelal Institute of Technology Business Management Studies

Contributor-Level 10

In all 74 recruiting companies were a part of the 2024 placement season at Jhulelal Institute of Technology. Refer to the table below for more:

Particulars	Placement Statistics (2024)
Companies Visited	74

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11 months ago

How are MBA placements at Jhulelal Institute of Technology?

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Delhi Pharmaceutical Sciences and Research University B.Sc

Contributor-Level 10

Jhulelal Institute of technology is yet to release its course wise placement statistics. Once available it will be mentioned here. Refer to the table below to know the overall placement highlights of Jhulelal Institute of Technology:

Particulars	Placement Statistics (2024)
No. of students placed	302
the highest Package	INR 12.36 LPA
Companies Visited	74
Placement Rate	77.78%

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11 months ago

What is the procedure to take BSc admission at DPSRU?

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Raushan Piplani

Contributor-Level 10

Delhi Pharmaceutical Sciences and Research University (DPSRU) BSc admission is based on merit in the last qualifying exam. Hence, the applicants performance in Class 12 or equivalent is considered. Students who are Class 12 or equivalent pass with at least 55% aggregate (50% aggregate for certain students) can apply for admission. After shortlisting, the university releases a merit list to declare names of selected students. These students can take part in counselling for seat allotment. Once allotment is done, the fee payment can be done for admission confirmation.

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11 months ago

27. Two godowns, A and B, have grain capacities of 100 quintals and 50 quintals, respectively. They supply to 3 ration shops, D, E and F, whose requirements are 60, 50 and 40 quintals respectively. The cost of transportation per quintal from the godowns to the shops is given in the following table:

Transportation Cost per Quintal (in Rs)
From/To	A	B
D	6	4
E	3	2
F	2.50	3

How should the supplies be transported in order that the transportation cost is minimum? What is the minimum cost?

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Jhulelal Institute of Technology

Contributor-Level 10

Let godown A supply x and y quintals of grain to shops D and E.

So, $(100 - x - y)$ will be supplied to shop F.

Since x quintals are transported from godown A, the requirement at shop D is 60 quintals. Hence, the remaining (60 – x) quintals will be transported from godown B.

Similarly, (50 – y) quintals and $40 - (100 - x - y) = (x + y - 60)$ quintals will be transported from godown B to shop E and F.

The given problem can be represented diagrammatically as given below:

$x \geq 0, y \geq 0, a n d 100 - x - y \geq 0$

Then, $x \geq 0, y \geq 0, a n d x + y \leq 100$

$\begin{array}{l} 60 - x \geq 0, 50 - y \geq 0, a n d x + y - 60 \geq 0 \end{array}$

$\begin{array}{l} T h e n, x \leq 60, y \leq 50, a n d x + y \geq 60 \end{array}$

Total transportation cost z is given by,

$\begin{array}{l} z = 6 x + 3 y + 2.5 (100 - x - y) + 4 (60 - x) + 2 (50 - y) + 3 (x + y - 60) \end{array}$

$\begin{array}{l} = 6 x + 3 y + 250 - 2.5 x - 2.5 y + 240 - 4 x + 100 - 2 y + 3 x + 3 y - 180 \end{array}$

$\begin{array}{l} = 2.5 x + 1.5 y + 410 \end{array}$

The given problem can be formulated as given below:

$M i n i m i s e z = 2.5 x + 1.5 y + 410 \dots \dots \dots \dots . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + y \leq 100 \dots \dots \dots . . (i i)$

$x \leq 60 \dots \dots \dots . . (i i i)$

$y \leq 50 \dots \dots \dots . (i v)$

$x + y \geq 60 \dots \dots \dots (v)$

$x, y \geq 0 \dots \dots \dots \dots . . (v i)$

The feasible region determined by the system of constraints is

...more

Let godown A supply x and y quintals of grain to shops D and E.

So, $(100 - x - y)$ will be supplied to shop F.

Since x quintals are transported from godown A, the requirement at shop D is 60 quintals. Hence, the remaining (60 – x) quintals will be transported from godown B.

Similarly, (50 – y) quintals and $40 - (100 - x - y) = (x + y - 60)$ quintals will be transported from godown B to shop E and F.

The given problem can be represented diagrammatically as given below:

$x \geq 0, y \geq 0, a n d 100 - x - y \geq 0$

Then, $x \geq 0, y \geq 0, a n d x + y \leq 100$

$\begin{array}{l} 60 - x \geq 0, 50 - y \geq 0, a n d x + y - 60 \geq 0 \end{array}$

$\begin{array}{l} T h e n, x \leq 60, y \leq 50, a n d x + y \geq 60 \end{array}$

Total transportation cost z is given by,

$\begin{array}{l} z = 6 x + 3 y + 2.5 (100 - x - y) + 4 (60 - x) + 2 (50 - y) + 3 (x + y - 60) \end{array}$

$\begin{array}{l} = 6 x + 3 y + 250 - 2.5 x - 2.5 y + 240 - 4 x + 100 - 2 y + 3 x + 3 y - 180 \end{array}$

$\begin{array}{l} = 2.5 x + 1.5 y + 410 \end{array}$

The given problem can be formulated as given below:

$M i n i m i s e z = 2.5 x + 1.5 y + 410 \dots \dots \dots \dots . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + y \leq 100 \dots \dots \dots . . (i i)$

$x \leq 60 \dots \dots \dots . . (i i i)$

$y \leq 50 \dots \dots \dots . (i v)$

$x + y \geq 60 \dots \dots \dots (v)$

$x, y \geq 0 \dots \dots \dots \dots . . (v i)$

The feasible region determined by the system of constraints is given below:

A (60, 0), B (60, 40), C (50, 50) and D (10, 50) are the corner points.

The values of z at these corner points are given below:

Corner Point	z = 2.5x + 1.5y + 410
A (60, 0)	560
B (60, 40)	620
C (50, 50)	610
D (10, 50)	510	Minimum

The minimum value of z is 510 at (10, 50).

Hence, the amount of grain transported from A to D, E, and F, is 10 quintals, 50 quintals and 40 quintals, respectively, and from B to D, E and F are 50 quintals, 0 quintals, 0 quintals, respectively.

Thus, the minimum cost is Rs. 510.

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11 months ago

How to crack the Jhulelal Institute of Technology placement interview?

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S. S. Jain Subodh Management Institute Jain Institute

Contributor-Level 10

To crack Jhulelal Institute of Technology placement interview students can follow the steps given below:

· Review your resume

· Practice common interview questions

· Showcase your strengths

· Be confident and articulate

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11 months ago

What is the procedure to take MBA admission at S S Jain Subodh Management Institute?

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Shailja Rawat

Contributor-Level 10

The S. S. Jain Subodh Management Institute MBA admission procedure commences with submission of an online application form. The form is available on the institute's official website. Students who fulfil the basic eligibility criteria are eligible to apply.

After closing the application portal, the admissions committee reviews all applications and shortlists students who meet the admission criteria set by the institute. Further, these shortlisted students are required to report to the institute for verification of documents and payment of fees.

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11 months ago

26. An aeroplane can carry a maximum of 200 passengers. A profit of ?. 1000 is made on each executive class ticket, and a profit of ?. 600 is made on each economy class ticket. The airline reserves at least 20 seats for executive class. However, at least 4 times as many passengers prefer to travel by economy class than by executive class. Determine how many tickets of each type must be sold in order to maximise the profit for the airline. What is the maximum profit?

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Delhi College Medicine & Health Sciences

Contributor-Level 10

Let the airline sell x tickets of executive class and y tickets of economy class, respectively.

The mathematical formulation of the given problem can be written as given below:

$M a x i m i s e z = 1000 x + 600 y \dots \dots \dots \dots (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + y \leq 200 \dots \dots \dots \dots \dots . . (i i)$

$x \geq 20 \dots \dots \dots \dots (i i i)$

$y - 4 x \geq 0 \dots \dots \dots \dots \dots (i v)$

$x, y \geq 0 \dots \dots \dots \dots \dots (v)$

The feasible region determined by the constraints is given below:

A (20, 80), B (40, 160) and C (20, 180) are the corner points of the feasible region.

The values of z at these corner points are given below:

Corner Point	z = 1000x + 600y
A (20, 80)	68000
B (40, 160)	136000	Maximum
C (20, 180)	128000

136000 at (40, 160) is the maximum value of z.

Therefore, 40 tickets of the executive class and 160 tickets of the economy class should be sold to maximise the profit, and the maximum profit is? 136000.

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11 months ago

Which is the No. 1 Pharmacy college in Delhi?

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Tasbiya Khan

Contributor-Level 10

As per NIRF ranking 2024, Jamia Hamdard emerged to be as the No. Pharmacy college in Delhi. Listed below are the colleges along with their NIRF rankings 2024:

College Name	NIRF 2022	NIRF 2023	NIRF 2024
Jamia Hamdard Ranking	1	2	1
Delhi Pharmaceutical Sciences and Research University Ranking	22	25	16

Disclaimer: This information is sourced from official website of the ranking body listed and may vary.

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11 months ago

25. A manufacturer makes two types of toys, A and B. Three machines are needed for this purpose, and the time (in minutes) required for each toy on the machines is given below:

Types of Toys	Machines
	I	II	III
A	12	18	6
B	6	0	9

Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is ?. 7.50 and that on each toy of type B is ?. 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.

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Jhulelal Institute of Technology Colleges in Nagpur

Contributor-Level 10

Let x and y toys of type A and type B be manufactured in a day, respectively.

The given problem can be formulated as given below:

$M a x i m i s e z = 7.5 x + 5 y \dots \dots \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} 2 x + y ? 60 \dots \dots \dots \dots . (i i)$

$x ? 20 \dots \dots \dots . . (i i i)$

$2 x + 3 y ? 120 \dots \dots \dots . . (i v)$

$x, y ? 0 \dots \dots \dots \dots \dots . (v)$

The feasible region determined by the constraints is given below:

A (20, 0), B (20, 20), C (15, 30) and D (0, 40) are the corner points of the feasible region.

The values of z at these corner points are given below:

Corner Point	z = 7.5x + 5y
A (20, 0)	150
B (20, 20)	250
C (15, 30)	262.5	Maximum
D (0, 40)	200

262.5 at (15, 30) is the maximum value of z.

Hence, the manufacturer should manufacture 15 toys of type A and 30 toys of type B to maximise the profit.

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11 months ago

Who were the top recruiters that participated during Jhulelal Institute of Technology placements?

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Rajiv Academy for Technology and Management Uttar Pradesh

Contributor-Level 10

Various companies visit Jhulelal Institute of Technology for placements some of them are given below:

Jhulelal Institute of Technology Placement: Top Recruiters
Amazon	TCS
Hexaware	HCL Technologies
QSpider	Accenture
Zensoft	Axis Bank

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11 months ago

What is the important date for getting admission in BCom at Rajiv Academy Mathura?

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Anushka Bidhi

Contributor-Level 10

Dates related to the admission portal opening and deadlines are important for students for participating in the admission process. The Class 12 result dates are also required to check for the fulfilling of eligibility criteria, set by college for admission into the BCom programme.

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11 months ago

Jhulelal Institute of Technology

What is the average package offered during Jhulelal Institute of Technology placements?

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Arizona State University Study Abroad

Contributor-Level 10

The average package for Jhulelal Institute of Technology has not been released. However, the highest package for 2024 is present in the table below:

Particulars	Placement Statistics (2024)
the highest Package	INR 12.36 LPA

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11 months ago

What are the career opportunities for the Arizona State University graduates?

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Shruti Mishra

Contributor-Level 7

As per the historical data of the university's alumni, most of the Arizona State University graduates get placed in industries such as:

Operations	Business Development	Education
Engineering	Sales	Information Technology
Community & Social Services	Arts & Design	Finance
Research	Media & Communication	Marketing
Human Resources	Consulting	Entrepreneurship

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11 months ago

Medicine & Health Sciences Delhi

How many top Pharmacy colleges are there in Delhi?

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Tasbiya Khan

Contributor-Level 10

There are around 2 top Pharmacy colleges in Delhi and both colleges are owned by the government organisations. Students can secure admission after passing Class 12 boards. Some of the best Pharmacy colleges in Delhi include Jamia Hamdard and Delhi Pharmaceutical Sciences and Research University.

Please refer to the table below for the best Pharmacy colleges in Delhi:

Parameters	Statistics
No. of Colleges	2 colleges
Annual Fee	INR 2-3 lakh: 1 college > INR 5 lakh: 1 college
Top Colleges	Jamia Hamdard and Delhi Pharmaceutical Sciences and Research University
Admission Process	Merit-based

Disclaimer: This information is sourced from official website and may vary.

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11 months ago

24. A dietician wishes to mix together two kinds of food, X and Y, in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. The vitamin contents of one kg of food are given below:

Food	Vitamin A	Vitamin B	Vitamin C
X	1	2	3
Y	2	2	1

One kg of food X costs ?. 16, and one kg of food Y costs ?. 20. Find the least cost of the mixture which will produce the required diet.

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S. S. Jain Subodh Management Institute Jain Institute

Contributor-Level 10

Let the mixture contain x kg of food X and y kg of food Y, respectively.

The mathematical formulation of the given problem can be written as given below:

$M i n i m i s e z = 16 x + 20 y \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + 2 y \geq 10 \dots \dots \dots \dots . (i i)$

$x + y \geq 6 \dots \dots \dots \dots (i i i)$

$3 x + y \geq 8 \dots \dots \dots \dots . (i v)$

$x, y \geq 0 \dots \dots \dots \dots (v)$

The feasible region determined by the system of constraints is given below:

A (10, 0), B (2, 4), C (1, 5) and D (0, 8) are the corner points of the feasible region.

The values of z at these corner points are given below:

Corner Point	z = 16x + 20y
A (10, 0)	160
B (2, 4)	112	Minimum

C (1, 5)	116
D (0, 8)	160

Since the feasible region is unbounded, 112 may or may not be the minimum value of z.

For this purpose, we draw a graph of the inequality, $16 x + 20 y < 112 o r 4 x + 5 y < 28$ , and check whether the resulting half-plane has points in common with the feasible region or not

...more

Let the mixture contain x kg of food X and y kg of food Y, respectively.

The mathematical formulation of the given problem can be written as given below:

$M i n i m i s e z = 16 x + 20 y \dots \dots . . (i)$

Subject to the constraints,

$\begin{array}{l} \end{array} x + 2 y \geq 10 \dots \dots \dots \dots . (i i)$

$x + y \geq 6 \dots \dots \dots \dots (i i i)$

$3 x + y \geq 8 \dots \dots \dots \dots . (i v)$

$x, y \geq 0 \dots \dots \dots \dots (v)$

The feasible region determined by the system of constraints is given below:

A (10, 0), B (2, 4), C (1, 5) and D (0, 8) are the corner points of the feasible region.

The values of z at these corner points are given below:

Corner Point	z = 16x + 20y
A (10, 0)	160
B (2, 4)	112	Minimum

C (1, 5)	116
D (0, 8)	160

Since the feasible region is unbounded, 112 may or may not be the minimum value of z.

For this purpose, we draw a graph of the inequality, $16 x + 20 y < 112 o r 4 x + 5 y < 28$ , and check whether the resulting half-plane has points in common with the feasible region or not.

Here, it can be seen that the feasible region has no common point with $4 x + 5 y < 28$ .

Hence, the minimum value of z is 112 at (2, 4).

Therefore, the mixture should contain 2 kg of food X and 4 kg of food Y.

The minimum cost of the mixture is ? 112.

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11 months ago

I have completed my MBA from S. S. Jain Subodh Management Institute. What jobs can I explore?

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Shailja Rawat

Contributor-Level 10

Once students have completed the MBA course offered by S. S. Jain Subodh Management Institute, they can explore jobs across various domains. Some of the popular domains often chosen by MBA graduates are Finance, Operations, Marketing, and Human Resources. The below table showcases some of the good-paying job profiles for MBA students:

Job Profiles for MBA Graduates
Business Analyst	Sales Manager
HR Manager	Asset Manager
Investment Banker	Sales Manager
Operations Manager	Management Consulting

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11 months ago

School of Dental Sciences (SDS), Sharda University Medicine & Health Sciences

What is the percentile required for admission at School of Dental Sciences (SDS), Sharda University?

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Pragati Taneja

Contributor-Level 10

School of Dental Sciences (SDS), Sharda University admissions are completely based on entrance-exam scores. Candidates can register online for admission to their preferred course. The candidate must meet the eligibility criteria set by the college. Aspirants must pass Class 12 for the UG courses and graduation for the PG courses. The eligibility criteria for the PhD course are to complete graduation with a 55% aggregate.

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11 months ago

Medicine & Health Sciences AIIMS

How can I get admission to AIIMS Paramedical after qualifying in CPET Paramedical?

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11 months ago

23. A farmer mixes two brands, P and Q of cattle feed. Brand P, costing ?. 250 per bag, contains 3 units of nutritional element A, 2.5 units of element B and 2 units of element C. Brand Q costing ?. 200 per bag, contains 1.5 units of nutritional element A, 11.25 units of element B, and 3 units of element C. The minimum requirements for nutrients A, B and C are 18 units, 45 units and 24 units, respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag. What is the minimum cost of the mixture per bag?

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