Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost (in dollars) associated with the new contra (Assume P, = number of PT-100 battery packs produced at the Philippines plant, P, = number of PT-200 battery packs produced at the Philippines plant, P, = number of PT-300 battery packs produced at the Philippines plant, M, number of PT-100 battery packs produced at the Mexico plant, M, = number of PT-200 battery packs produced at the Mexico plant, M, = number of PT-300 battery packs produced at the Mexico plant.) 1.10P, +1.13P, + 1.49P, +1.06M, + 1.14M, + 1.23M3 Min s.t. P, +M, 2 202,000| PT-100 Production P2+ M, 2 102,000 PT-200 Production PT-300 Production P3+ M3 2 148,000 P1+P,<175000 Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant M + M, 5 160000 Ps 75000 PT-300 Production Mexico Plant PT-300 Production Philippines Plant M35 100,000 M,, M2, Mg, Pz. Pz. P3 z 0 ) Solve the linear program developed in part (a) to determine the optimal production plan. (M2, M2, M3, P4, P2, P3) = 40000,100000,50000,160000,0,100000 ) What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.) $ 524,100

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(a) Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost (in dollars) associated with the new contract.
(Assume P, = number of PT-100 battery packs produced at the Philippines plant, P, = number of PT-200 battery packs produced at the Philippines plant, P, = number of PT-300 battery packs produced at the Philippines plant, M, =
number of PT-100 battery packs produced at the Mexico plant, M, = number of PT-200 battery packs produced at the Mexico plant, M, = number of PT-300 battery packs produced at the Mexico plant.)
Min 1.10P, + 1.13P2+1.49P3+1.06M1+1.14M, +1.23M3
s.t.
Р, + M, 2 202,000
PT-100 Production
P,+ M, > 102,000
PT-200 Production
PT-300 Production
P3 + M, > 148,000
Pi+P,<175000
Р, +
2
Combined PT-100 and PT-200 Production Mexico Plant
Combined PT-100 and PT-200 Production Philippines Plant
M, + M, < 160000
P3575000
PT-300 Production Mexico Plant
PT-300 Production Philippines Plant
M3 < 100,000
M1, M2, M3, P, P2, P3 2 0
(b) Solve the linear program developed in part (a) to determine the optimal production plan.
(M1, M2, M3, P1, P2, P3) =
40000,100000,50000,160000,0,100000
What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.)
$ 524,100
(c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT-100 in the Philippines plant.
It would have to decrease by more than $ 0.04
X per unit.
Transcribed Image Text:(a) Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost (in dollars) associated with the new contract. (Assume P, = number of PT-100 battery packs produced at the Philippines plant, P, = number of PT-200 battery packs produced at the Philippines plant, P, = number of PT-300 battery packs produced at the Philippines plant, M, = number of PT-100 battery packs produced at the Mexico plant, M, = number of PT-200 battery packs produced at the Mexico plant, M, = number of PT-300 battery packs produced at the Mexico plant.) Min 1.10P, + 1.13P2+1.49P3+1.06M1+1.14M, +1.23M3 s.t. Р, + M, 2 202,000 PT-100 Production P,+ M, > 102,000 PT-200 Production PT-300 Production P3 + M, > 148,000 Pi+P,<175000 Р, + 2 Combined PT-100 and PT-200 Production Mexico Plant Combined PT-100 and PT-200 Production Philippines Plant M, + M, < 160000 P3575000 PT-300 Production Mexico Plant PT-300 Production Philippines Plant M3 < 100,000 M1, M2, M3, P, P2, P3 2 0 (b) Solve the linear program developed in part (a) to determine the optimal production plan. (M1, M2, M3, P1, P2, P3) = 40000,100000,50000,160000,0,100000 What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.) $ 524,100 (c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit (in dollars per unit) would have to change to produce additional units of the PT-100 in the Philippines plant. It would have to decrease by more than $ 0.04 X per unit.
Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium-ion battery packs for a new line of phones. The contract calls for the
following.
Battery Pack
Production Quantity
PT-100
202,000
PT-200
102,000
РТ-300
148,000
Photon Technologies can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage
rates. The unit costs for each battery pack at each manufacturing plant are as follows.
Product
Philippines
Мexico
PT-100
$0.95
$0.98
PT-200
$0.98
$1.06
PT-300
$1.34
$1.15
Transcribed Image Text:Photon Technologies, Inc., a manufacturer of batteries for mobile phones, signed a contract with a large electronics manufacturer to produce three models of lithium-ion battery packs for a new line of phones. The contract calls for the following. Battery Pack Production Quantity PT-100 202,000 PT-200 102,000 РТ-300 148,000 Photon Technologies can manufacture the battery packs at manufacturing plants located in the Philippines and Mexico. The unit cost of the battery packs differs at the two plants because of differences in production equipment and wage rates. The unit costs for each battery pack at each manufacturing plant are as follows. Product Philippines Мexico PT-100 $0.95 $0.98 PT-200 $0.98 $1.06 PT-300 $1.34 $1.15
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