Rate of Return and Non-negativity Constraints
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 the highest profit. Use the corner point graphical approach. Let X1 = the number of air conditioners scheduled to be produced X2 = the number of fans scheduled to be produced Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity constraint) | | 2X1 | + | X2 | ≤ | 140 | (drilling capacity constraint) | | | | X1, X2 | ≥ | 0 | (non-negativity constraints) |
Optimal Solution: X1 = 40 X2 = 60 Profit = $1,900
7-15 Electrocomp’s management realizes that it forgot to include two critical constraints (see Problem 7-14). In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred an oversupply of fans in the preceding period, management also insists that no more than 80 fans be produced during this production period. Resolve this product mix problem to find the new optimal solution. Let X1 = the number of air conditioners scheduled to be produced X2 = the number of fans scheduled to be produced
Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity
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 the highest profit. Use the corner point graphical approach. Let X1 = the number of air conditioners scheduled to be produced X2 = the number of fans scheduled to be produced Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity constraint) | | 2X1 | + | X2 | ≤ | 140 | (drilling capacity constraint) | | | | X1, X2 | ≥ | 0 | (non-negativity constraints) |
Optimal Solution: X1 = 40 X2 = 60 Profit = $1,900
7-15 Electrocomp’s management realizes that it forgot to include two critical constraints (see Problem 7-14). In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred an oversupply of fans in the preceding period, management also insists that no more than 80 fans be produced during this production period. Resolve this product mix problem to find the new optimal solution. Let X1 = the number of air conditioners scheduled to be produced X2 = the number of fans scheduled to be produced
Maximize | 25X1 | + | 15X2 | | | (maximize profit) | Subject to: | 3X1 | + | 2X2 | ≤ | 240 | (wiring capacity