Quasar Enterprise use overtime, inventory, and subcontracting to absorb fluctuations in demand, An annual production plan is devised and updated quarterly. Expected demand over the next four quarters is 600, 800, 1600 and 1900 units, respectively. The capacity for regular production is 1000 units per quarter with an overtime capacity of 100 units per quarter. Subcontracting is limited to 500 units a quarter. Regular production costs $20 per unit, overtime $25 per unit, and subcontracting $30 per unit. Inventory holding costs are assessed at $3 per unit per period. There is no beginning inventory. Design a production plan that will satisfy demand at minimum costs. What is the minimum cost?
In your answer, please derive and show the minimizing equation/objective function as well as the demand and supply constraints. Then use Excel and the solver add-in to build and solve the problem.