Solution Key Average = Range 9 to 25. BOSTON COLLEGE GRADUATE SCHOOL OF MANAGEMENT Operations and Strategic Management Department

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1 Solution Key Average. Range 9 to BOSTON COLLEGE GRADUATE SCHOOL OF MANAGEMENT Operations and Strategic Management Department MD76 Modeling and Decision Analysis Spring 00 Quiz This quiz is printed on both sides the page. There are a total questions (labeled a-e). Valu-Com Electronics manufactures five different models telecommunications interface for personal and laptop computers. As summarized in the following table each these devices requires differing amounts printed circuit (PC) board resistors memory chips and assembly Per Unit Requirements HyperLink FastLink SpeedLink MicroLink EtherLink PC Board (square inches) Resistors Memory Chips Assembly Labor (in hours) The unit wholesale price and manufacturing cost for each model are as follows. Per Unit Revenues and Costs HyperLink FastLink SpeedLink MicroLink EtherLink Wholesale Price $89 $9 $9 $69 $9 Manufacturing Cost $6 $0 $96 $7 $0 In their net production period Valu-Com has square inches PC board resistors 0000 memory chips and 000 hours assembly time available. They can sell all the product they can manufacture but the marketing department wants to be sure they produce at least 00 units each product and at least twice as many FastLink as HyperLink while maimizing prit.

2 Valu-Com has formulated the following linear program. Let 0 0 or Subject to 8 8 Maimize EtherLink MicroLink SpeedLink FastLink HyperLink

3 a. Before solving this model (i.e. answer this question without referring to the attached answer report or sensitivity report) Valu-Com management proposes the following: Last period we produced 00 FastLink and 70 each the other four? Is this solution feasible? Why or why not? Can this solution possibly be optimal? Why or why not? 0(70)(00)0(70)8(70)(70)70< < < <000 all s>00 00(70) binding This solution is feasible (all constraints are satisfied). The solution lies on the constraint. It can only be optimal if there are alternate optimal solutions. However if Valu- Com simply produces one more FastLink the prit goes up and all constraints are still satisfied (in this case none are binding). In addition it can be seen that the objective function and binding constraint are not parallel. b. Valu-com management now makes the following recommendation (again answer this question without referring to the attached answer report and sensitivity report) HyperLink are the most pritable why don t we produce00 HyperLink and 00 FastLink and 70 each the other three? Is this solution feasible? Why or why not? Can this solution possibly be optimal? Why or why not? < >00000 not feasible 00>0000 not feasible 67.<000 all s>00 00<(00) not feasible This solution is not feasible and therefore can not be optimal.

4 c. Valu-Com management is not satisfied with the solutions above. To remedy this they solve the linear programming model using Ecel and solver. Attached are the Ecel spreadsheet solver answer report and solver sensitivity report. What is the optimal each type card that Valu-Com should produce? How many assembly hours will they use? How much prit will this product mi yield? From the answer report: Produce 00 HyperLink 000 FastLink 00SpeedLink 0 MicroLink 00 EtherLink Use 687. assembly hours Yield $000 in prit d. Valu-Com management had forecasted prit for the period to be $000. They are concerned that investors will react negatively to their missing this forecast. Valu- Com believes that they can obtain either more PC board or more memory chips by borrowing from net period s inventory. (You can assume that Valu-Com is not concerned about the impact this may have on net period s prit.) Should they borrow PC board? Why or Why not? If yes how much should they borrow to reach their prit forecast? Should they borrow memory chips? Why or Why not? If yes how many should they borrow to reach their prit forecast? They should not borrow PC board because they already have ecess (see slack in answer report). The should borrow memory chips (less than the allowable increase). Each chip contributes $7.0 to prit. This will increase total prit to $000$7.0()$00.

5 e. Valu-Com has heard a rumor that HyperLink are going to become an industry standard. This is likely to drive the price HyperLink up. How much will the wholesale price HyperLink have to increase before Valu-Com should consider producing more HyperLink Cards? Eplain. (Answer this question independent question d.) The price HyperLink must go up by at least $.67. This can be seen from the allowable increase for the HyperLink contribution to prit or the shadow price on the HyperLink production constraint.

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