Reference no: EM133075103

ABC Ltd signed a contract with an electronics company to produce three different products, X, Y, and Z. The contract calls for the following quantities to be produced:

Product Production Quantity

X 200,000

Y 100,000

Z 150,000

ABC Ltd can manufacture the three products at plants located in two countries. The unit cost of products differs at the two plants because of differences in production requirement and wage rates. The unit costs for each product at each manufacturing plant are as follows:

Product Plant in Country 1 Plant in Country 2

X $0.95 $0.98

Y $0.98 $1.06

Z $1.34 $1.15

Products X and Y are produced using similar production equipment available at both plants. However, each plant has a limited capacity for the total number of X and Y produced. The combined X and Y production capacities are 175,000 units in Country 1 and 160,000 units in Country 2. The third (Z) product capacities are 75,000 and 100,000 units, respectively. The cost of shipping from the plant in Country 1 is $0.18 per unit, and the cost of shipping from the plant in Country 2 is $0.10 per unit.

a. Develop a linear program (LP) that ABC Ltd can use to determine how many units of each product to produce at each plant in order to minimize the total production and shipping cost associated with this contract.

b. Solve the LP developed in p. 1 to determine the optimal production plan. Fully interpret your answer.

c. Suppose that the cost of producing one unit of X at the plant in Country 1 decreased by $0.04. Will the optimal solution found in p. (b) change? Fully explain and justify your answer.

d. Ignore the change in p. (c) above. Assume now that ABC Ltd could easily and immediately increase their capacity for Z production in Country 2 from 100,000 units to 120,000 units at an additional cost of $0.20 per each additional unit produced. Should they do that? Will this decision allow them to further minimize their objective function? Fully explain and justify your answer.