Page 1 - WORKSHEETS

XII-CHAPTER-12

WORK SHEET

1. The objective function of a LPP is

a) a constant
b) a function to be optimized
c) a relation between the variables
d) none of these

2. The optimal value of the objective function is attained at the points

a) On x-axis
b) On y-axis
c) which are corner points of the feasible region

d) None of these

3. One kind of cake requires 200g flour and 25g of fat, and another kind of cake requires 100g
of flour and 50g of fat. Find the maximum number of cakes which can be made from 5 kg of
flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making
the cakes?

4. Maximize Z = 3x + 2y

Subject to x + 2y ≤ 10, 3x + y ≤ 15, x, y ≥ 0.

5. Minimize and Maximize Z = 5x + 10y

Subject to x + 2y ≤ 120, x + y ≥ 60, x − 2y ≥ 0, x ≥ 0, y ≥ 0.

6. A factory manufactures two types of screws, A and B. Each type of screw requires the use of
two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6
minutes on hand operated machines to manufacture a package of screws A, while it takes 6
minutes on automatic and 3 minutes on the hand operated machines to manufacture a package
of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer
can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs10.Assuming that
he can sell all the screws he manufactures, how many packages of each type should the factory
owner produce in a day in order to maximize his profit? Determine the maximum profit.