LINEAR PROGRAMMING FORMULATION PROBLEMS AND SOLUTIONS
7-14 The Electro comp 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 Electro comp’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
Electro comp 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 constraint)
2X1 + X2 ≤ 140 (drilling capacity constraint)
X1 ≥ 20 (a/c contract constraint)
X2 ≤ 80 (maximum # of fans constraint)
X1, X2 ≥ 0 (non-negativity constraints)
Optimal Solution: X1 = 40 X2 = 60 Profit = $1,900
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
7-14 The Electro comp 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 Electro comp’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
Electro comp 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 constraint)
2X1 + X2 ≤ 140 (drilling capacity constraint)
X1 ≥ 20 (a/c contract constraint)
X2 ≤ 80 (maximum # of fans constraint)
X1, X2 ≥ 0 (non-negativity constraints)
Optimal Solution: X1 = 40 X2 = 60 Profit = $1,900
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
