Sony, a television company, has three major departments for the manufacture of its two models, A and B. The monthly capacities are given as follows: the marginal profit per unit from model A is birr 400 and that of model B is birr 1000. Assuming that company can sell any quantity of either product due to favorable market conditions, determine the optimum output for both the models, the highest possible profit for this month and the slack time in the three departments.

Considering the two models A and B manufactured at the three Major departments

Although your question has some missing values below are the missing details ;

Time required by model A :  4,  2.5,  4.5

Time required by model B :  2,  1,  1.5

Hours available this month : 1,600, 1,200, 1,600  for departments I, II and III

The marginal profit per unit from model A is 40 RO and that of model B is 10 RO

1) calculate the optimum output for both models

first step : express the problem as a Linear program problem

variables = a , b

objective ; maximize  [tex]40a + 10b[/tex]

The constraints can be expressed as ;

[tex]4a + 2b <= 16002.5a + 1b <= 12004.5a + 1.5b <= 1600[/tex]

resolving these constraints using excel solver as attached below

The optimum output  : model A = 355.56 ,  model B = 0

2 ) The highest possible profit ( max ) = $14,222.22 using the excel solver attached below

3) The slack time in the three departments

The slack time is the difference the left hand side and the right hand side in a constraints table

Given that: LHS < RHS for depart 1 and 2

The slack times are :  Depart 1 = 1600 - 14222.22 = 177.78 hours ≈ 178 hours

                                   Depart 2 = 1200 - 888.89 = 311.11 hours ≈ 311 hours

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Cold in the earth—and the deep snow piled above thee,
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5 Now, when alone, do my thoughts no longer hover
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