Suppose that a Company has regular production capacity to produce 200 Vans per week. Assume that with overtime an additional 25 cars per week can be produced. The cost of assembly and inspecting a car during regular time is $2000. Overtime production of a van costs $3500. It also costs $500 per week to hold a car in inventory for future delivery. The company's order schedule for the next 6 weeks is : 215,150,165,225,195,225. Their goal is to provide quality service and do not want any shortages. Create a production schedule that will determine how much regular and overtime production needs for the next 6 weeks while also minimizing its cost. Assume there is no inventory on hand at the beginning of week 1. Sole this production problem using Excel Solver.

a. What is the optimal production schedule? What is the number of cars held in inventory each week, if any?

b. Proposal: If the weekly overwork capacity is increased by 15 cars to a total of 40 cars per week for a fixed payment of $10000. Should the Company take the deal?

c. Without resolving. What is the largest fixed payment such that the proposal is profitable for the Company ? Can you guess in which weeks would the extra overwork capacity be used, if any?