Question

Blue Ridge Hot Tubs manufactures and sells two models of hot tubs: the Aqua-Spa and the Hydro-Lux. Howie Jones, the owner and manager of the company, needs to decide how many of each type of hot tub to produce during his next production

Answer 1

Answer:

a lot is missing in this question, so I looked for a similar one:

Howie buys prefabricated fiberglass hot tub shells from a local supplier and adds the pump and tubing to the shells to create his hot tubs.  (This supplier has the capacity to deliver as many hot tub shells as Howie needs.)  Howie installs the same type of pump into both hot tubs.  

He will have only 200 pumps available during his next production cycle.  From a manufacturing standpoint, the main difference between the two models of hot tubs is the amount of tubing and labor required.  Each Aqua-Spa requires 9 hours of labor and 12 feet of tubing.  Each Hydro-Lux requires 6 hours of labor and 16 feet of tubing.  Howie expects to have 1,520 production labor hours and 2,650 feet of tubing available during the next production cycle.   Howie earns a profit of $350 on each Aqua-Spa he sells and $300 on each Hydro-Lux he sells.

you have to maximize the following equation: 350A + 300H

where:

A = number of Aqua-Spa hot tubs sold

H = number of Hydro-Lux hot tubs sold

the constraints are:

A + H ≤ 200

9A + 6H ≤ 1,520

12A + 16H ≤ 2,650

A ≥ 0

B ≥ 0

both A and B are integers

Using solver, the optimal solution is: 117A + 77B, and the maximum profit = $64,050