Optimal production plan, computer manufacturer. Information Technology, Inc. assembles and sells two products: printers and desktop computers. Customers can purchase either
(a) A computer or
(b) A computer plus a printer.
The printers are not sold without the computer. The result is that the quantity of printers sold is equal to or less than the quantity of desktop computers sold. The contribution margins are $240 per printer and $120 per computer. Each printer requires 7.2 hours’ assembly time on production line 1 and 12 hours’ assembly time on production line
2. Each computer requires 4.8 hours’ assembly time on production line 1 only. (Many of the components of each computer are preassembled by external vendors.) Production line 1 has 28.8* hours of available time per day. Production line 2 has 24 hours of available time per day. Let X represent units of printers and Y represent units of desktop computers. The production manager must decide on the optimal mix of printers and computers to manufacture.*Line 1 is actually two parallel lines, each used 14.4 hours per day. To simplify calculations, count as one line with 28.8 hours.
1. Express the production manager’s problem in an LP format.
2. Which combination of printers and computers will maximize the operating income of Information Technology? Use both the trial-and-error and the graphic approach.