Question

Neptunite Baryte (NB) produces two models of children’s climbers, Toddler and Junior. Sales of Toddler provide a $15 contribution margin per climber; sales of Junior provide a $20 contribution margin per unit. All children’s climbers are started in the Forming Department and completed in the Finishing Department. In the Forming Department a special type of super strength bamboo is used for climber formation. Due to global shortages, NB cannot get more than 2,000 meters of this bamboo per month. The Toddler model requires 1 meter of bamboo per climber and the Junior model requires 1.5 meters. Special machinery in the Finishing Department cannot be used more than 3,000 hours per month. Both models require 2 hours per climber with this machinery to finish. NB can sell as much as it can produce of Toddler but cannot sell more than 750 climbers of Junior per month.

REQUIRED:

1.       What is Neptunite Baryte’s objective function? (1 mark)

2.       State the equations that represent Neptunite Baryte’s constraints?

         

3.       Determine the product mix that will maximize the constrained           resources.   

4.       At the point determined above, how much profit will be made? (1 mark)

Answer 1

	X - No. of units of Toddler
	Y - No. of units of Junior
	Objective Functions
1	Profit = 15X+20Y
2	Constraints Equations
	X>=0
	Y>=0
	1X+1.5Y<=2000
	2X+2Y<=3000

1X +1.5Y =2000
1X = 2000-1.5Y	Equation -1
2X+2Y=3000
X+Y=1500	Equation -2
Substitute Equation -1 in Equation - 2
X+Y=1500
2000-1.5Y +Y =1500
0.5Y = 500
Y = 1000 units
Y = 1000 units in Equation -2
X= 500 units
Maximum Profit = (15*500)+(20*1000)
$                          27,500.00