LP slides #$2325$: Blue Ridge Hot Tubs $($Mathematical Formulation$)$

Blue Ridge Hot Tubs manufactures two models: Aqua$-$Spa and Hydro$-$Lux.

Howie Jones needs to decide how many of each model to make to maximize profits. He earns the profits of $$350$ on each Aqua$-$Spa and $$300$ on each Hydro$-$Lux.

Each tub requires one pump. Aqua$-$Spa requires $9$ hours of labor. Hydro$-$Lux requires $6$ hours of labor. Howie has only $200$ pumps and $1,566$ production hours available.

Write the LP formulations of the problem:

Decision Variables:

Let Xa be the number of aqua$-$spa to make and

Xh be the number of hydro$-$lux to make

Enter the following numbers corresponding to the object function and each constraint

Enter $1$ if your answer is: $1$Xa $+1$Xh $<=200$

Enter $2$ if your answer is: $9$Xa $+6$Xh $<=1566$

Enter $3$ if your answer is: Xa $>=0,$ Xh $>=0$

Enter $4$ if your answer is: Maximize Total profits $=350$Xa $+300$ Xh

The objective function is: $4$

The equation for the labor hours constraint is: $2$

The equation for the pump constraint is: $1$

The non$-$negativity constraints: $3$

LP slides #$2325$: Blue Ridge Hot Tubs $($Solve$)$

Set up the problem in Excel and use Solver to solve for the optimal solutions.

Note: Do not put a comma or any non$-$numeric character in your answers.

The optimal number of aqua$-$spa to produce is

units

The optimal number of aqua$-$spa to produce is

units

The optimal $($maximum$)$ total profit is $

$.$

How many labor hours are used to produce the optimal number of hot tubs?

hours

Which resource$($s$)$ are used up$?$

Enter $1$ if your answer is: labor hour

Enter $2$ if your answer is: pump

Enter $3$ if your answer is: both

Answer: