Question

A business manufactures four products (A, B, C, D), each requiring a number of input materials for production. Information on each of the products, including selling price and profit margin per unit, demand per week, and the number of each input required to produce one unit of product is provided below.

It has been found that the business does not have enough stabilizing brackets to meet the full demand for all four products, and must thus find the “product mix” that maximizes profit. Please find the optimal product mix.  How many units of Product D will the optimal product mix include?

ProductA Products Product ProductD Selling Price 125 $ 135 5 150 $ 175 - Variable Cost 60 $ 65 $ 90 $ 95 = Profit Margin/Unit $ 65 $ 70 $ 60 $ 80 Demand 60 70 25 45 $ $ Number of input materials required for each unit of production Total Input Material ProductA Product Product ProductD Required Cross-beams 1 1 2 2 270 Butterfly clamps 16 20 24 28 4,220 Stabilizing brackets 9 10 12 15 2,215 Articulating hinges 2 6 6 960 Total Available 400 12,000 1,495 1,200

Answer 1

A constraint is a limiting factor to organization's performance, an obstacle to the organization achieving its goal.

As given Stabilizing bracket is the contraints as all the other material are available in suffiecient quantity hence product mix will be find by Contribution or Profit per constrain t activity

Calcultion of Contribution per stabilizing bracket and ranking product

	Product A	Product B	Product C	Product D
Profit Margin per unit(a)	$65	$70	$60	$80
Stablizing Bracket required per unit (b)	9	10	12	15
Profit Margin per Bracket (a÷b)	$7.22	$7	$5	$5.33
Ranking based on above profit margin	(i)	(ii)	(iv)	(iii)

Calcuation of Unit that can be produce based on above ranking

Product ( Based on Ranking)	Unit Demand	Stabilzing Bracket Required	Stabilizing Bracket Remains	Unit Produce
A	60	(60×9)=540	1495-540 =955	60
B	70	70×10=700	=955-700 =255	70
D	45	255	0	255/15=17
C	25	0	0	0

Hence 17 unit of Product D will be included in optimal product mix.