Question 1(14 marks)

A small furniture manufacturer produces three products. Each product must go through three stages of the manufacturing process: assembly, finishing, and inspection. The assembly time, finishing time, and inspection time for each unit of each product are provided in the table below. The unit cost, selling price, and the minimum demand for each product are also provided.

Hours required to produce one unit

Product 1

Product 2

2.5 1.5 0.5

Product 3

3 2.5 1.5

$50 $23040

To keep a balance, the number of product 1 units produced should be at least twice the number of product 2 units. Also, the number of product 3 units cannot exceed three times the number of product 2 units.

Assembly time3Finishing time2Inspection time1Cost per unit

Selling Price per unit

The minimum demand (units)

Available hours

600 550 195

$70 $265100

$60 $25050

1

SCMA 2000-01.06-F21

1) Formulate a linear programming model for this problem. Clearly define the variables, objective function, and constraints. [5]

2) Solve the problem using Excel or Excel QM and answer the following questions: a) What is the optimal solution to this LP problem? [7]

b) Would the optimal solution change if the Selling Price of Product 1 increases by $50 and all other Products are unchanged? Explain. [2]