Answer :
Option a) Linear Program Model - P1, P2, P3, M1, M2, M3 [tex]\geq[/tex] 0
Option b) Total Production and shipping cost = $524,100
Option c) Shipping cost decreased by = $0.04
Option d) Shipping cost per unit be decreased by = $0.05
According to the question given,
P1 = PT-100
P2 = PT-200
a) Linear Program Model could be shown as,
P1 = Number of PT-100 models
P2 = Number of PT-200 models
P3 = Number of PT-300 models
M1 = Number of PT-100 products
M2 = Number of PT-200 products
M3 = Number of PT-300 products
Calculations of the objectives =
(0.95+0.51)P1 + (0.98+0.15)P2 + (1.34+0.15)P3 + (0.98+0.08)M1 + (1.06+0.08)M2 + (1.15+0.08)M3
Summing the models and products in order,
P1 + M1 Greater than and equal to 200000
P2 + M2 greater than and equal to 100000
P3 + M3 greater than and equal to 150000
P1 + P2 less than and equal to 175000
M1 + M2 less than and equal to 160000
P3 less than and equal to 75000
M3 less than and equal to 100000
⇒ P1, P2, P3, M1, M2, M3 [tex]\geq[/tex] 0
b) Using the Exel Solver
Decision Variable Value
P1 40000
P2 100000
P3 500000
M1 160000
M2 0
M3 100000
Total Production and shipping cost = $524,100
c) In the objective coefficient P1 is 0.04 so the shipping cost per unit will be decreased by $0.04
d) Since the allowance is decreased in M2 is 0.05 so the cost per unit will be decreased by $0.05
Therefore,
Option a) Linear Program Model - P1, P2, P3, M1, M2, M3 [tex]\geq[/tex] 0
Option b) Total Production and shipping cost = $524,100
Option c) Shipping cost decreased by = $0.04
Option d) Shipping cost per unit be decreased by = $0.05
To learn more about Probability,
https://brainly.com/question/24756209
#SPJ4
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-100 200,000
PT-200 100,000
PT-300 150,000
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:
Plant
Product Philippines Mexico
PT-100 0.95 0.98
PT-200 1.34 0.98
PT-300 1.06 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 $0.15 per unit, and the cost of shipping from the Mexico plant is 0.08 per unit.
(a) Develop a linear program that Photon Technologies can use to determine how many units of each battery pack to produce at each plant to minimize the total production and shipping cost associated with the new contract.
(b) Solve the linear program developed in part (a), to determine the optimal production plan. Qty Produced Philippines Mexico PT-100 16000c 40000 PT-200 100000 0 5000 1000 PT-300 Total Cost-$
(c) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional units of the PT-100 in the Philippines plant. If required, round your answer to two decimal digits At least $ / unit.
(d) Use sensitivity analysis to determine how much the production and/or shipping cost per unit would have to change to produce additional units of the PT-200 in the Mexico plant. If required, round your answer to two decimal digits. At least $ .05/ unit.
