Linear Programming Formulation

Modelfly, Inc., which manufactures remote control model aircraft, wishes to determine a production schedule for the next four months. The sales forecasts indicate that demand requirements for May, June, July, and August are 5000, 10000, 3000, and 7000 units, respectively. There were 3000 units produced during April and there are 2000 units in inventory at the end of April. The per unit cost of increasing production from one month to the next is $3.50 per unit. The per unit cost of decreasing production from one month to the next is $2.00 per unit. Storage limitations require that ending inventory does not exceed 3000 units in any month. Production should never increase by more than 40% from one month to the next. Formulate a linear programming model that will establish a production schedule for May-August with the objective of minimizing the costs of increasing and decreasing production.