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 may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit.
Now, Electrocomp’s management also realizes that there should be a minimum number of air conditioners produced in order to fulfill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced.
1. If Electrocomp decides that at least 20 air conditioners should be produced but no more than 80 fans should be produced, the optimal production mix of air conditioners and fans is __________. (The first number is for air conditioners and the second for fans.)
A. (50,30)
B. (20,80)
C. (40,60)
D. (26.67,80)
2. In the optimal solution for the above question (Question 1), the slack for the four constrains — Total hours of wiring, Total hours of drilling, Number of air conditioners, Number of fans are __________, respectively. (Hint: A negative number shows that the constraint is binding downward, i.e. it sets a lower rather than an upper limit. You may take the negative sign out when interpreting the results.)
A. 0, 0, 20, 20
B. 0, 0, 10, 20
C. 0, 0, 20, 10
D. 10, 10, 10, 10
3. If Electrocomp decides that at least 30 air conditioners should be produced but no more than 50 fans should be produced, the optimal production of air conditioners is ______ and the optimal production of fans is _______ . (Please only enter an integer and include no units.)
4. In the optimal solution for the above question (Question 3), the slack for the four constrains — Total hours of wiring, Total hours of drilling, Number of air conditioners, Number of fans are __________, respectively. (Hint: A negative number shows that the constraint is binding downward, i.e. it sets a lower rather than an upper limit. You may take the negative sign out when interpreting the results.)
A. 0, 0, 15, 10
B. 5, 0, 15, 0
C. 0, 5, 15, 0
D. 0, 0, 10, 15