(Electro Corporation) The Electro Corporation manufactures two electrical products: air conditioners and 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, at most 240 hours of wiring time are available and at most 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate an LP of this product mix problem to find the best combination of air conditioners and fans for the highest total profit.
(Electro Corporation) The Electro Corporation manufactures two electrical products: air conditioners and 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, at most 240 hours of wiring time are available and at most 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate an LP of this product mix problem to find the best combination of air conditioners and fans for the highest total profit.
max pX 1 + qX 2 (Total profit)
s.t. aX 1 + bX 2 u (Wiring)
cX 1 + dX 2 v (Drilling)
X 1, X 2 0
(Hint: Let X1 = number of air conditioners and X2 = number of fans)
In this question, we could see that there are two products, these are air conditioners and fans. Here, there are two constraints, which are wiring and drilling, we would determine the total number of air conditioners and the total number of fans which would maximize the total profit value. Hence, This Product mix problem would deal with the Maximization of profits.
This question has been asked for only the LP formulation of the product mix problem,
The LP formulation is done in the next section.
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
