"Linear programing( industrial engineering) Videocomp, Inc., a new manufacturer of cathode ray tube devices (CRT's) for computer applications, is planning to enlarge its capacity over the next two years. The company's primary objective is to grow as rapidly as possible over these two years to make good on its marketing claims. The CRT's are produced in sets of 200 units on modular assembly lines. It takes three months to produce a set of 200 units from initial chemical coating to nal assembly and testing. To ensure quality control, none of the units in a set is shipped until the entire set has been completed. Videocomp has three modular assembly lines and thus currently can produce up to 600 units per quarter. Each set of 200 units requires $15,000 at the beginning of the quarter when the production is initiated for purchasing component parts and paying direct labor expenses. Each set produces revenue of $35,000, of which 20% is received at the time of shipment and the remaining 80% a full three months later. Videocomp has negotiated the terms for adding modular assembly lines with a number of contractors and has selected two possible contractors. The rst contractor requires an investment of $60,000 paid in advance and guarantees that the assembly line will be completed in three months. For the same assembly line, the second contractor requires an investment of $20,000 in advance and an additional investment of $20,000 upon completion; however, his completion time is six months. The present assets of Videocomp for investment in new modular assembly lines and nancing current operations are $150,000. No further funds will be made available except those received from sales of CRT's. However, as the market is expanding rapidly, all CRT's produced can be sold immediately.

Formulate a linear program to maximize Videocomp's productive capacity at the end of two years
using eight planning periods of three months duration each. Should any of the variables restricted to be integer?