A manufacturing firm produces two products. Each product must undergo an assembly process and a finishing process. It is then transferred to the warehouse, which has space for only a limited number of items. The firm has 80 hours available for assembly and 112 hours for finishing, and it can store a maximum of 10 units in the warehouse. Each unit of product 1 has a profit of $30 and requires 4 hours to assemble and 14 hours to finish. Each unit of product 2 has a profit of $70 and requires 10 hours to assemble and 8 hours to finish. The firm wants to determine the quantity of each product to produce in order to maximize profit.
a. Formulate a linear programming model for this problem (find the decision variables, constraints, the objective function)
b. What type of linear programming model does this problem belong to?
c. Solve this model using Excel.
d. Is 3 units of product 1 and 7 units of product 2 a feasible solution? Why?
e. Is 6 units of product 1 and 5 units of product 2 a feasible solution? Why?
f. What is your recommendation based on your solution?