LP slides #$23-25$: Blue Ridge Hot Tubs $($Solve$)$ LP slides #$23-25$: 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: $1xa+1xh200$

Enter $2$ if your answer is: $9xa+6xh1566$

Enter $3$ if your answer is: $xa0,xh0$

En LP slides #$23-25$: 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

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

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

hours

units

units

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:

Answer $1$:

$122$

Answer $2$:

$83$

Answer $3$:

$61000$

Answer $4$:

$1566$

Answer $5$:

$3$ter $4$ if your answer is: Maximize Total profits $=350xa+300xh$

The objective function is:

The equation for the labor hours constraint is:

The equation for the pump constraint is:

The non$-$negativity constraints:

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

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

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

hours

units

units

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:

Answer $1$:

$122$

Answer $2$:

$83$

Answer $3$:

$61000$

Answer $4$:

$1566$

Answer $5$:

$3$