Problem 4 Please, thank you so much We used the example of the Product Mix model

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Problem 4 Please, thank you so much

We used the example of the Product Mix model from the textbook. But mind that some numbers are changed here. PC Tech company assembles and then tests eight models of computers, including model 1 to model 8. For the coming month, the company wants to decide how many of each model to assemble and then test. No computers are in inventory from the previous month, and because these models are going to be changed after this month, the company does not want to hold any inventory after this month. All necessary input variables and the objective are shown in the following excel spreadsheet. PC Tech wants to know how many of each model it should produce (assemble and test) to maximize its net profit, but it cannot use more labor hours than are available, and it does not want to produce more than it can sell. Therefore, an LP model was employed to know the maximum total net profit while meeting the constraints. and testing computers per labor hour assembling Cost per labor hour testing. line cost per labor ho"tesn%ine2 inputs for ansembling and testing a computer Model 1 Model 2 Model 3 Model 4 Model5 Model&Model7; Model abor hours for assembly Labor hours for testing, Ine abor hours for nesting, Ine 5s 2.5 s.s 2.5 335 25 3.5 Cost of component parts eling prce 50 $225 $22s $225 $250$0 $250 $300 200 214.00 $13400 $14.00 $230.00 S185.00 $190.00 5171.00 19.00 527,50 $127 50 $167.50 79 0 5174.00 $166.50 Unt margin, tested on ine 2 testing plan of co sa Model 1 Model 2 Model 3Model 4 Model 5 Model Model7 Mode 1500 1250 Number tested on ine 2 Tosal computers produced 1500 1250 450 1000 Censtraints (hours per month Hours ned Hours available valiablity for assembling abor avelability for testing line evaelablity fer beting in2 8125 et proft 15 per month) Tested on ne ested on ine2 308.250 $267 300 so $21,750 so so $397,300 90 550 544 5304 300258. 856 438

Explanation / Answer

a)

A bindind constrint is defind as the variable with slack variable = 0 such that the difference of Final value and Constraint R.H. Side would be zero otherwise non binding

There are 11 constraints,

b)

If the reduced cost is zero, there will be no effect on optimal value of objective function if the number varies within allowable limit.

In line 1 Model 4, the reduced cost is zero and the allowable decrease is 1.9. Hence there will be no effect on objective function if the number decreases upto 1.9.

c)

Here the reduced cost = - 40

Allowable increase = 40

The optimal value of objective function will decrease by 40 for one unit increase. And the objective function will be unaffected upto increase of 40. ( Upto allowable limit optimal value will change while the objective function will be same)

d)

The shadow price for a constraint can be define as the change in the optimal value of the objective function for one unit increase in the resource (righthand-side value) for that constraint

Shadow Price for total computers prodeuced of Model 1 = 66.625.

Allowable Increase = 166.66667

Allowable Decrease = 1000

Hence the optimal value of objective function will increase by 66.625 for one unit increase of Right hand Side upto value 166.66667 and will decrease by 66.625 for one unit decrease of Right hand Side upto value 1000.

e)

Shadow Price for assambly hour = 33.5

Allowable increase = 4000 > 4

Hence optimal value will increase by ( 4*33.5 = ) 135

f)

When the labor avalibility for assambly hours used is increase or decrease outside the limit bound, we have to re run the model.

When number of hours increase more than 4000 or number of hour decrease less than 1625 we have to rerun the model

Constraint Final Value Constrint R. H. Side Difference 1 1500 1500 0 Binding 2 1250 1250 0 Binding 3 0 1250 1250 Non Binding 4 450 1250 800 Non Binding 5 1000 1000 0 Binding 6 0 1000 1000 Non Binding 7 0 1000 1000 Non Binding 8 0 800 800 Non Binding 9 20000 20000 0 Binding 10 5000 5000 0 Binding 11 3812.5 6000 2187.5 Non Binding

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