Question

An electronics corporation manufactures three models of TV sets, models A, B, and C. There are three stages in the manufacturing process and the number of hours per set is given in the following table. Hours Per set Model Assembly Wiring Testing A 0.2 0.2 0.1 B 0.3 0.2 0.2 с 0.1 0.2 0.1 a.) Define your variables. b.) Write the objective function. c.) Write the constraints. d.) Set up the initial simplex tableau. The profits on the three models are $60, $80, and $70 respectively. The hours available for assembly, wiring, and testing are 40, 28, and 16 hours respectively. How many of each model should be made in order to maximize total profit?

Answer 1

(A)

Let number of model A TV sets = x

Let number of model B TV sets = y

Let number od model C TV sets = z

(B)

Objective functions:

Maximize Z = 60x + 80y + 70z

(C)

Constraints :

0.2x + 0.3y + 0.1z ≤ 40 (assembly constraint)

0.2x + 0.2y + 0.2z ≤ 28 (Wiring Constraint)

0.1x + 0.2y + 0.1z ≤ 16 (Testing constraint)

x, y, z ≥ 0

After introducing slack variables::

Constraints:

0.2x + 0.3y + 0.1z + s1 = 40

0.2x + 0.2y + 0.2z + s2 = 28

0.1x + 0.2y + 0.1z + s3 = 16

x, y, z, s1, s2, s3 ≥ 0

(D)

Initial simplex tableau:

	Cj	60	80	70	0	0	0
Cb	Basics	x	y	z	s1	s2	s3	b
0	s1	0.2	0.3	0.1	1	0	0	40
0	s2	0.2	0.2	0.2	0	1	0	28
0	s3	0.1	0.2	0.1	0	0	1	16