Question
Asked Oct 25, 2019
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What is the maximum profit in this model?

A manufacturing company wants to maximize profits on products A, B, and C. The profit margin is $3 for A, $6 for B, and
$15 for C. The production requirements and departmental capacities are as follows:
Department Production requirement Departmental capacity
by product (hours)
Ав с
(Total hours)
Assembling
Painting
Finishing
2 3 2
30,000
1
2 2
38,000
28,000
2
3
1
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A manufacturing company wants to maximize profits on products A, B, and C. The profit margin is $3 for A, $6 for B, and $15 for C. The production requirements and departmental capacities are as follows: Department Production requirement Departmental capacity by product (hours) Ав с (Total hours) Assembling Painting Finishing 2 3 2 30,000 1 2 2 38,000 28,000 2 3 1

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Expert Answer

Step 1

Assume the manufacturing company manufactures x1 units of product A, x2 units of product B and x3 units of product C.

Find below the given information,

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Max z 3x, 6x, +15x with the constraints 2x 3x2x 30000 2x, 2x 38000 2x +3xx28000 where

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Step 2

In the above problem, use the slack variable

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Max z 3x, 6x, +15x 0.5 +0.S2 +0.S with the constraints 2x 3x2x3 + S = 30000 2x 2x S = 38000 2x, +3xxS, 28000 where, S,,S2,S 2 0 x

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Step 3

Using the simplex method, to find the maximum profi...

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000 CJ 3 6 15 Minimum ratio в | Сз Хs SSS XB 030000 S2038000 0 100 2 2 15000 010 00 1 00 1 1 2 2 19000 S0 28000 28000 2 1 0 0 0 -3-615 0 0 0 z, -C

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