# Question: a company needs to devise a production plan over the...

###### Question details

A company needs to devise a production plan over the planning horizon of the next T weeks such that a known demand is satisfied and the total production and inventory cost is minimized. Suppose the known demand of week t is dt, and let c P t and c I t denote the cost of producing one unit of the company’s product in week t and the cost of carrying one unit of the product in inventory from week t to t + 1, respectively. The production capacity of the company is U units per week, and there is no inventory storage limit. As of now, the company has I0 units of product in inventory. Formulate an LP, solving which gives an optimum (minimumcost) production plan for this company. (Hint: a production plan exactly specifies how many products will be in inventory at the beginning of week t, how many products should be produced in this week, and consequently how many products will remain in inventory at the end of this week after satisfying the demand.)