Question

The next two questions are based on the following case: A manufacturer of hot tubs makes two kinds of hot tubs Wishy and Washy. Wishy requires 7 hours of labor and Washy requires 8 hours. Wishy needs 50 feet of tubing and Washy needs 40 feet. The manufacturer expects to have 1500 labor hours and 9000 feet of tubing available. A single hot tub of type Wishy requires 2 pumps whereas type Washy requires 3 pumps. He has 500 pumps at his disposal. He expects to make a profit of $70 on each type of hot tub Wishy he sells and $50 on Washy Let X- the number of Wishy bathtubs and Y- the number of Washy bathtubs manufactured. 5. The Objective Function for the LP problem is: a. Max 50 X+70Y b. Min 70X+50Y c. Max 70X 50Y d. Max 70X+50Y 2

Answer 1

5) 1 unit of Wishy hot tub gives a profit of $70 and 1 unit of Washy hot tub gives a profit of $50

The manufacturer will always want to maximise his profits

If X and Y denotes the number of wishy and washy bathtubs manufactured then, the total profit is 70X+50Y which is to be maximised.

$\therefore$ The objective function is

Max 70X+50Y

6) The given information can be summarised as follows:

Resources	Requirements		Availability
	Wishy(X)	Washy(Y)
Labor (hours)	07	08	1500
Tubing (feet)	50	40	9000
Pump	02	03	500

Thus, the constraint corresponding to labor is

$\dpi{150} \fn_cm 7X+8Y\leq 1500$