LINEAR PROGRAMMING
LEVEL UP WORKSHEET
1. There are two types of fertilisers A and B’. A’ consists of 12% nitrogen and 5% phosphoric acid whereas B’
consists of 4% nitrogen and 5% phosphoric acid. After testing the soil conditions, farmer finds that he needs at
least 12 kg of nitrogen and 12 kg of phosphoric acid for his crops. If ‘A’ costs 110 per kg and B’ costs ₹ 8 per kg,
then graphically determine how much of each type of fertiliser should be used so that the nutrient requirements
are met at a minimum cost?
2. To supplement daily diet, a person wishes to take X and Y tablets. The contents (in milligrams per tablet) of iron,
calcium and vitamins in X and Y are given as below:
The person needs to supplement at least 18 milligrams of iron, 21 milligrams of calcium and 16 milligrams of
vitamins. The price of each tablet of X and Y is ₹ 2 and ₹ 1, respectively. How many tablets of each type should
the person take in order to satisfy the above requirement at the minimum cost? Make an LPP and solve
graphically.
3. A company manufactures three kinds of calculators: A B and C in its two factories I and II. The company has got
an order for manufacturing at least 6400 calculators of kind A 4000 of kind B and 4800 of kind C. The daily output
of factory I is of 50 calculators of kind A 50 calculators of kind B and 30 calculators of kind C. The daily output of
factory II is of 40 calculators of kind A 20 of kind B and 40 of kind C. The cost per day to run factory I is ₹ 12000
and of factory II is ₹ 15000. How many days do the two factories have to be in operation to produce the order
with the minimum cost? Formulate this problem as an LPP and solve it graphically.
4. A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting
machine and a sprayer. It takes 2 hr on the grinding/cutting machine and 3 hr on the sprayer to manufacture a
pedestal lamp. It takes 1 hr on the grinding/cutting machine and 2 hr on the sprayer to manufacture a shade. On
any day, the sprayer is available for at the most 20 hr and the grinding/cutting machine for at most 12 hr. The
profit from the sale of a lamp is ₹ 25 and that from a shade is ₹ 15. If the manufacturer can sell all the lamps and
shades that he produces, how should he schedule his daily production to maximise his profit? Formulate an LPP
and solve it graphically.
5. A dietician wishes to mix two types of foods in such a way that the vitamin content of the mixture contains at
least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units per kg of vitamin A and 1 unit per kg of
vitamin C. Food II contains 1 unit per kg of vitamin A and 2 units per kg of vitamin C. It costs ₹ 50 per kg to
purchase food I and ₹ 70 per kg to purchase food II. Formulate the problem as a linear programming problem to
minimise the cost of such mixture and find the minimise cost graphically.
6. A merchant plans to sell two types of personal computers, a desktop model and a portable model that will cost
₹ 25000 and ₹ 40000, respectively. He estimates that the total monthly demand of computers will not exceed
250 units. Determine the number of units of each type of computers which the merchant should stock to get
maximum profit, if he does not want to invest more than ₹ 70 lakh and his profit on the desktop model is ₹ 4500
and on the portable model is ₹ 5000. Make an LPP and solve it graphically.
