Question

1. A company wants to determine how many units of each of two products, A and B, they should produce. The profit on product A is $50 and the profit on product B is $45. Applying linear programming to this problem, which of the following is the objective function if the firm wants to make as much money as possible?

1. Maximize Z = A/45B + B/50A
2. Minimize Z = 50 A + 45 B
3. Maximize Z = A + B                       
4. Minimize Z = A + B
5. Maximize Z = 50 A + 45 B

2. An agribusiness company mixes and sells chicken feed to farmers. The costs of the chicken feed ingredients vary throughout the chicken feeding season but the selling price of chicken feed is independent of the ingredients. On August 1, management needs to know how many units of each of three grains (Q, R, and S) should be included in their chicken feed in order to produce the product most economically. The cost of each grain is, for a unit of Q, $30; for a unit of R, $37; and for a unit of S, $78. Applying linear programming to this problem, which of the following is the objective function?

1. Minimize Z = (Q × R × S)/3
2. Maximize Z = Q + R + S
3. Minimize Z = 30 Q + 37 R + 78 S
4. Minimize Z = Q + R + S
5. Maximize Z = 30 Q + 37 R + 78 S

3. Apply linear programming to this problem. A firm wants to determine how many units of each of two products (products D and E) they should produce to make the most money. The profit in the manufacture of a unit of product D is $100 and the profit in the manufacture of a unit of product E is $87. The firm is limited by its total available labor hours and total available machine hours. The total labor hours per week are 4,000. Product D takes 5 hours per unit of labor and product E takes 7 hours per unit. The total machine hours are 5,000 per week. Product D takes 9 hours per unit of machine time and product E takes 3 hours per unit. Which of the following is one of the constraints for this linear program?

1. 9 D + 3 E = > 4,000
2. 5 D + 7 E = < 5,000
3. 5 D + 7 E = 4,000
4. 5 D + 9 E = < 5,000
5. 9 D + 3 E = < 5,000

Answer 1

Q1) The objective function is
e. Maximize Z = 50 A + 45 B

The objective is to maximize the total profit

Q2)
The objective is to minimise the total cost.Therefore, objective function is
c.Minimize Z = 30 Q + 37 R + 78 S

Q3)
The maximum possible machine hours is 5000. Following is a constraint
e.9 D + 3 E = < 5,000