Question

PDC Spa, Inc. manufactures and sells two spa models: The Premium and the Lifestyle. PDC Spa receives spa body part assemblies from other producers and then adds tubing and a pump circulate the water. The Premium model demands 14.75 hours of labor and 13.65 feet of tubing. The Lifestyle model requires 11.45 hours of labor and uses 18.95 feet of tubing. According to the selling records, the owner, Bo Fan, has determined that the Premium model generates a profit of $450 per unit, and the Lifestyle model generates $380 profit. Although Bo would like to maximize the utilization of labor capacity and sufficient tubing and pumps to build any number of spas, his resources are limited. For the next production period, Bo has 2,760 labor hours, 3,654 feet of tubing, and 230 pumps available.

Question: Bo needs your assistance in figuring out how many Premium and Lifestyle models to build in order to maximize his profit?

Answer 1

This is a profit maximiztion problem ,

with 3 veriables i will show equetion below and after solving those equation answer will be fetched however it i have solved below equations through excel solver.

Profit * no. of product a + profit *no . of b shall be maximised.

where

labour hr *no. of a +lab hrs in b*no of B <= 2760

tubing ft in a *no. of A +tubint ft in b*no of b produced <= 3654

after solving this in excel solver i have got below results.

	PREMIMUM	LIFESTYLE
No. of pumps	85	131
			TOTAL	AVAILABLE
PROFIT	450	380	88030
LABOUR HOURS	14.75	11.45	2753.7	2760
TUBE FEET	13.65	18.95	3642.7	3654

hence no. of premium 85 and no of lifestyle shall be 131 to maximise the profit and at this point maxium profit will be $ 88030 .