Smalltime Investments Inc is going to purchase new computers. There are ten employees, and the company would like one for each employee
The cost of the basic personal computer with monitor and disk drive is $2,000, while the deluxe version with VGA and advanced processor is $3,500. Due to internal politics, the number of deluxe computers should be less than half the number of regular computers, but at least three deluxe computers must be purchased. The budget is $27,000, although additional money could be used if it were deemed necessary. All of these are goals that the company has identified. Formulate this as a goal programming problem.
Let R = number of regular computers purchased
D = number of deluxe computers purchased
d1- = underachievement of goal of 10 computers to purchase
d1+ = overachievement of goal of 10 computers to purchase
d2- = unused budget
d2+ = additional monies required
d3- = underachievement of goal of the number of deluxe computers should be less than half the number of regular computers
d3+ = overachievement of goal of the number of deluxe computers should be less than half the number of regular computers
d4- = underachievement of goal that the number of deluxe computers should be at least 3
d4+ = overachievement of goal that the number of deluxe computers should be at least 3
Minimize d1- + d1+ + d3+ + d4-
Subject to: R + D + d1- - d1+ = 10
2000R + 3500D + d2- - d2+ = 27,000
-0.5R + D + d3- - d3+ = 0
D + d4- - d4+ = 3
all variables ? 0
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