A customer requires during the next four months respectively 50, 65, 100, and 70 units of a commodity (no backlogs allowed). Productions costs are $5, $8, $4, and $7 per unit during these months. The storage cost from one month to the next are $2 per unit (assessed on the end of the month inventory). Each unit at the end of the month 4 could be sold for $15/unit. The production capacities for each month are 90, 75, 80, and 50 units respectively. Currently, there are 15 units in inventory. Formulate a Linear Program that will minimize the objective function (sum of the production and inventory costs revenue from selling end of period inventory at month 4). Note, inventory cost is assessed only for the first 3 periods. Model and solve the problem in AMPL and answer the quiz.