An air conditioning company manufactures three home air conditioners: model A, model A+ and model A++. The profits per unit are $70, $100, and $145, respectively. The production requirements per unit and the availability of the three resources are given below:
|
Model A
|
Model A+
|
Model A++
|
Available
|
|
Number of fans
|
1
|
1
|
1
|
400
|
|
Number of cooling coils
|
2
|
2
|
4
|
600
|
|
Manufacturing Time
|
12
|
16
|
20
|
4500 hours
|
(a) If the profit from a unit of model A+ increases from $100 to $110, will the optimal number of units of the three models manufactured change? Will the total profit change? What will be the new optimal number of units of the three models and the new profit?
(b) The company has an opportunity to obtain some extra manufacturing time. What is the maximum price the company should pay for each additional hour of manufacturing time, and how many hours of manufacturing time should they obtain at that price?
(c) The company has an opportunity to buy some extra fans. What is the maximum price the company should pay for each additional fan, and how many fans should they buy at that price?