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	201,000
PT-200	102,000
PT-300	149,000

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	Mexico
PT-100	$0.95	$0.98
PT-200	$0.98	$1.06
PT-300	$1.34	$1.15

The PT-100 and PT-200 battery packs are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of PT-100 and PT-200 battery packs produced. The combined PT-100 and PT-200 production capacities are 175,000 units at the Philippines plant and 160,000 units at the Mexico plant. The PT-300 production capacities are 75,000 units at the Philippines plant and 100,000 units at the Mexico plant. The cost of shipping from the Philippines plant is $0.18 per unit, and the cost of shipping from the Mexico plant is $0.10 per unit.

(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 P₁ = number of PT-100 battery packs produced at the Philippines plant, P₂ = number of PT-200 battery packs produced at the Philippines plant, P₃ = number of PT-300 battery packs produced at the Philippines plant, M₁ = number of PT-100 battery packs produced at the Mexico plant, M₂ = number of PT-200 battery packs produced at the Mexico plant, M₃ = number of PT-300 battery packs produced at the Mexico plant.)

Min _________ s.t.

PT-100 Production ____________

PT-200 Production ____________

PT-300 Production ____________

Combined PT-100 and PT-200 Production Mexico Plant ____________

Combined PT-100 and PT-200 Production Philippines Plant ____________

PT-300 Production Mexico Plant ____________

PT-300 Production Philippines Plant ____________

M₁, M₂, M₃, P₁, P₂, P₃ 0

(b)

Solve the linear program developed in part (a) to determine the optimal production plan.

(M₁, M₂, M₃, P₁, P₂, P₃) = (____________)

What is total cost of the production plan (in dollars). (Round your answer to the nearest dollar.)

$______________

(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 $ ____________ per unit.

(d)

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-200 in the Mexico plant.

It would have to decrease by more than $ ____________ per unit.