Question

. A merchant has 9000 square feet of floor space for storing units of products 1 and 2. To gain the advantage of a good price he must purchase his stock now. A unit of product 1 costs the merchant $6 and requires 2 square feet of space, while a unit of product 2 costs the merchant $3 and requires 3 square feet of space. The merchant must stock at least 500 units of product 1. He expects to make a profit of $2 from each unit of product 1 he stocks and $4 from each unit of product 2. He is instructed to stock no less than 5000 total units of the products. The amount of product 1 that he stocks should be no more than half the amount of product 2 that he stocks. He has $10000 available for purchasing stock, and wants to know how many units of each product to buy to maximize profit. Create the LP model for this problem and use it to answer questions 1 to 5. How many decision variables are in this problem?

A none listed

B 0

C 3

D 4

E 5

F 2

2. How many constraints are there in above problem. Do not include trivial constraints.

A 1

B 2

C 3

D 4

E 5

F none of the answers listed here

3. How many of the constraints are less than or equal to constraints?

A 0

B 4

C 5 or more

D 1

E 2

F 3

4. Which of the following is the correct constraint?

A. X1 + .5X2 greater than or equal to 0

B. None of the answers are given

C. X1 - 2x2 less than or greater than 0

D. X1 - .5X2 less than or equal to 0

E. -.5X1 +X2 less than or equal to 0

5. The objective function is.

A none of the answers given here

B x1 + 4x2

C x1 + x2 + x3 less than or equal to 300

D 6x1 + 3x2

E x1 + 500x2

F x1 + x2

Answer 1

The answer of the above questions are as follows

• 1. F. 2 Decision Variables = 1)Total No. of units for Product 1 and 2) Total no of units for Product 2
• 2. E. 5 The constraints are, 1) Space available per square feet, 2)the total number of products should be more than 5000 units, 3)the amount of product 1 that he stocks should be no more than half the amount of product 2 that he stocks, 4) he has only $10000 available to be spend and 5) There should be at least 500 units of Product 1.
• 3. F.3 The constraints are : 1) Space available should be less than 9000 square feet, 2) The total cost of the inventory should be $10000 and 3) the amount of product 1 that he stocks should be no more than half the amount of product 2 that he stocks,
• 4. D. X1 - .5X2 less than or equal to 0. This represents that the number of units of Product 1 should be less than half the number of units of Product 2.
• 5. A. None of the answers given here. The objective function of the question is to maximize the profit. Therefore the objective would be Z= 2x1 + 4x2