The management of a company is considering three possible new products for next year’s product line. A decision now needs to be made regarding which products to market and at what production levels.

Initiating the production of two of these products would require a substantial start-up cost, as shown in the first row of the table below. Once production is under way, the marginal net revenue from each unit produced is shown in the second row. The third row gives the percentage of the available production capacity that would be used for each unit produced.

Only 3 units of product 1 could be sold, whereas all units that could be produced of the other two products could be sold. The objective is to determine the number of units of each product to produce in order to maximize the total profit (total net revenue minus start-up costs).

(a) Assuming that production quantities must be integers, use dynamic programming to solve this problem.

(b) Now consider the case where the divisibility assumption holds, so that the variables representing production quantities are treated as continuous variables. Assuming that proportionality holds for both net revenues and capacities used, use dynamic programming to solve this problem.