Production Planning for Components Rummel Electronics produces two PC cards, a modem and a network adapter. Demand for these two products exceeds the amount that the firm can make, but there are no plans to increase production capacity in the short run. Instead, the firm plans to use subcontracting. The two main stages of production are fabrication and assembly, and either step can be subcontracted for either type of card. However, the company policy is not to subcontract both steps for either product. (That is, if modem cards are fabricated by a subcontractor, then they must be assembled in-house.) Components made by subcontractors must pass through the shipping and receiving departments, just like components made internally. At present, the firm has 5200 hours available in fabrication, 3600 in assembly and 3200 in shipping/inspection. The production requirements, in hours per unit, are given in the following table.

The direct material costs for the modem cards are $3.25 for manufacturing and $0.50 for assembly; for network cards, the costs are $6.10 and $0.50. Subcontracting the manufacturing operation costs $5.35 for modem cards and $8.50 for network cards. Subcontracting the assembly operation costs $1.50 for either product. Modem cards sell for $20, and network cards sell for $28. The firm's policy, for each product, is that at most 40 percent of the units produced can have subcontracted fabrication, and at most 70 percent of the units can have subcontracted assembly.

(a) Determine the production and subcontracting schedule that will maximize profits, given that Rummel Electronics wishes its schedule to contain an integer number of units produced and subcontracted.

(b) Solve the problem without the integer restrictions. What is the solution? By how much (in percentage terms) do the restrictions alter the value of the optimal objective function?