Question

At a chip manufacturing plant, four technicians, (A, B, C, D) produce three products (Products 1, 2, and 3). This month, the chip manufacturer can sell 80 units of Product 1, 50 units of Product 2 and, at most, 50 units of Product 3. Technician A can make only Product 1 and 3. Techncian B can make only Products 1 and 2. Technician C can make only Product 3. Techncian D can make only Product 2. For each unit produced, the products contribute the following profit: Product 1, $6, Product 2, $7, Product 3, $10. The time (in hours) each technician needs to manufacture a product is as follows:

Product	Technician A	Technician B	Technician C	Technician D
1	2	2.5	Cannot Do	Cannot Do
2	Cannot Do	3	Cannot Do	3.5
3	3	Cannot Do	4	Cannot Do

               

Each technician can work up to 120 hours per month. How can the chip manufacturer maximize it’s monthly profit? Assume a fractional number of units can be produced.

Answer 1

Excel solver , we write following formula in constraint set : =I4*I7+J4*J7+K4*K7 ( and similar formula for other constraints)

Objective function :  =I4*I5+J4*J5+K4*K5

I J K L M N

Decsn variables		x1	x2	x3
		15	27.5	30
Contribution		6	7	10	582.5
						Capcity
Constraint		1	0	0		80	15
		0	1	0		50	27.5
		0	0	1		50	30
		2	0	3		120	120
		2.5	3	0		120	120
		0	0	4		120	120
		0	3.5	0		120	96.25