During the next four months, a customer requires, respectively, 500, 650, 1000, and 700 units of a commodity, and no backlogging is allowed (that is, the customer's requirements must be met on time). Production costs are $50, $80, $40, and $70 per unit during these months. The storage cost from one month to the next is $20 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 can be sold for $60. Assume there is no beginning inventory.
a. Determine how to minimize the net cost incurred in meeting the demands for the next four months.
b. Use SolverTable to see what happens to the decision variables and the total cost when the initial inventory varies from 0 to 1000 in 100-unit increments. How much lower would the total cost be if the company started with 100 units in inventory, rather than none? Would this same cost decrease occur for every 100-unit increase in initial inventory?