Section B: Linear Programming (Worth 25 marks)

CHIEF Electronics Corporation manufactures four complex products that it supplies to aerospace firms. Each of the products must pass through the following departments before they are shipped: wiring, drilling, assembly, and inspection. The time requirement in hours for each unit to be produced and its corresponding profit value are summarized in the following table:

Department	Unit profit
Product	Wiring	Drilling	Assembly	Inspection
A	0.5	0.3	0.2	0.5	9
B	1.5	1	4	1	12
C	1.5	2	1	0.5	15
D	1	3	2	0.5	11

The capacity available in each department each month, and the minimum monthly production requirement to fulfill contracts, are as follows:

Department	Full capacity (hours)	Available capacity (% of full capacity)
Wiring	18,750	80
Drilling	34,000	50
Assembly	52,000	50
Inspection	16,000	75

Product	Minimum production level
A	150
B	100
C	300
D	400

You, as the production manager, have the responsibility of specifying production levels for each product for the coming month.

B.1. Formulate the problem as a LP model and then solve it by using Excels Solver. Explain/interpret the solution obtained. (10 marks)

CHIEF Electronics Corporation
	Recycling	Water Storage	Water Management
Decision Variables	x1	x2	x3	x4
	20650	100	2750	400
Objective funtion (Max)	9	12	15	11	232700
Constraints
Wiring Hours	0.5	1.5	1.5	1	15000	<=	15000
Drilling Hours	0.3	1	2	3	12995	<=	17000
Assembly Hours	0.2	4	1	2	8080	<=	26000
Inpection Hours	0.5	1	0.5	0.5	12000	<=	12000
A	1				20650	>=	150
B		1			100	>=	100
C			1		2750	>=	300
D				1	400	>=	400

B.3. If there is a shortage of 20% in the available capacity of the inspection department, should you keep the solution you found or change it? Why or why not? (5 marks)