# Types of Linear Programing Problems

## Trending Questions

**Q.**A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of 80 on each piece of type A and 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

**Q.**Solve the following problem:

Maximize Z=−Px1+4x2

Subject to: −3x1+x2≤6

x1+2x2≤4

x2≤−3

No lower bound constraint for x1

**Q.**The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs □20 per kg and sand costs of □6 per kg. Strength consideration dictates that a concrete brick should contain minimum 4 kg of cement and not more than 2 kg of sand. Form the LPP for the cost to be minimum.

**Q.**A company manufactures two articles A and B. There are two department through which these article are processed : (i) assembly and (ii) finishing department. The maximum capacity of the first department is 60 hours a week and that of other department. 48 hours, per week. The product of each unit of article A requires 4 hours in assembly and 2 hours in finishing and that of each unit of B requires 2 hours in assembly and 4 hours in finishing. If the profit is Rs. 6 for each unit A and Rs. 8 for each unit of A and Rs. 8 for each unit of B, find the number of units of A and B to be produced per week in order to have maximum profit.

**Q.**A firm manufactures two products A and B. Each product is processed on two machines M1 and M2. Product A requires 4 minutes of processing time on M1 and 8 min. on M2; product B requires 4 minutes on M1 and 4 min. on M2. The machine M1 is available for not more than 8 hrs 20 min. while machine M2 is available for 10 hrs during any working day. The products A and B are sold at a profit of Rs. 3 and Rs. 4 respectively.

Formulate the problem as a linear programming problem and find how many product of each type should be produced by the firm each day in order to get maximum profit.

**Q.**Minimise Z=3x+2y

subject to constraints:

x+y≥8

3x+5y≤15

x≥0, y≥0

**Q.**Dietician has to develop a special diet using two foods P and Q. Each packet (containing 30 g) of food P contains 12 units of calcium, 4 units of iron, 6 units of cholesterol and 6 units of vitamin A, while each packet of the same quality of food Q contains 3 units of calcium, 20 units of vitamin A. The diet requires atleast 240 units of calcium, atleast 460 units of iron and almost 300 units of cholesterol. How many packets of each food should be used to maximize the amount of vitamin A in the diet? What is the maximum amount of vitamin A?

**Q.**Corner points of the bounded feasible region for an LP problem are A(0, 5)B(0, 3)C(1, 0)D(6, 0). Let z=−50x+20y be the objective function. Minimum value of z occurs at ______ center point.

- (0, 5)
- (6, 0)
- (0, 3)
- (1, 0)

**Q.**A firm has the cost function C=x33−7x2+111x+50 and demand function x=100−p.

Write the total revenue function in terms of x

**Q.**Minimize Z=x+2y

Subject to the constraints

2x+y≥3

x+2y≥6

and x≥0, y≥0