Problem 4: A,B and C please We used the example of the Product Mix model from th

Question

Problem 4: A,B and C please

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

solving first 4

a)

we can see that labour availability for testing line 2 is not binding as it's value is 3182<6000

b)

reduced cost tells us how much change will be in the objective function if we force the variable to be non zero

so for item 4 line 1 we get reduced cost as 0 as the optimized value is >0

c)

for item 3 line 2 the optimal solution is 0 but if we force the value to be non 0 we will have the objective function will decrease by 40 or profit will decrease by 40

d)

shadow price tess us how much the objective function will change if the rhs is changed

so for every extra unit of model 1 allowed profit will increase by 66

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