Essay about Rate of Return and Non-negativity Constraints

4465 Words Dec 12th, 2012 18 Pages
LINEAR PROGRAMMING FORMULATION PROBLEMS AND SOLUTIONS

7-14 The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time maybe used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields
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Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? Use the graphical LP approach.

Let X1 = the number of benches produced X2 = the number of tables produced

Maximize | 9X1 | + | 20X2 | | | (maximize profit) | Subject to: | 4X1 | + | 6X2 | ≤ | 1,200 | (labor hours constraint) | | 10X1 | + | 35X2 | ≤ | 3,500 | (redwood capacity constraint) | | | | X1, X2 | ≥ | 0 | (non-negativity constraints) | Optimal Solution: X1 = 262.5 X2 = 25 Profit = $2,862.50

7-18 The dean of the Western College of Business must plan the school’s course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college an average of $2,500 in faculty wages, and each graduate course costs $3,000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum? Let X1 = the number of undergraduate courses scheduled X2 = the number of graduate courses scheduled Minimize | 2,500X1 | + | 3,000X2 | | | (minimize faculty salaries) | Subject to: | X1 | | | ≥ | 30 | (schedule

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