Question

Power Recreation assembles two engines, a snowmobile engine and a boat engine, at its
Lexington, Kentucky, plant.
Snowmobile Engine Boat Engine
Selling Price $800 $1,000
Variable cost per unit 560 625
Contribution margin per unit $240 $375
Contribution margin percentage
($240 ÷ $800; $375 ÷ $1,000)
30% 37.5%
Assume that only 600 machine-hours are available daily for assembling engines. Additional
capacity cannot be obtained in the short run. Power Recreation can sell as many boat engines 4
as it produces but the demand for snowmobile engines is limited to be 200 engines per day.
The constraining resource, then, is machine-hours. It takes two machine-hours to produce one
snow mobile engine and five machine-hours to produce one boat engine.
Required:
A. Which product should power recreation emphasise?
B. What product mix should Power Recreation’s managers choose to maximize its
operating income? Show your analysis

Answer 1

Answer:

Explanation:

a) Objective function: Max 240Q + 375B (maximize total contribution margin from sale of Quad bikes and Boat engines)

Constraints:

2Q + 5B <= 600   (available capability in assembly dept)

1Q + 0.5B <= 120 (available capacity in testing dept)

B <= 110

Q, B >= 0

b) Graphical representation  

c) Corner points

Corner points Q B Z

Intersection of C3 and B-axis 0 110 41,250

Intersection of C1 and C3 25 110 47,250

Intersection of C1 and C2 75 90 51,750

Intersection of C2 and Q-axis 120 0 28,800

Optimal solution: Q = 75, B = 90

Total contribution margin = $ 51,750

d)

i) Refer the sentivity report output of Excel, Allowable increase for objective coefficient of Quad bike is 510. Therefore, increase of $ 50 is within the allowable range of increase. Hence optimal mix would not change.

ii) Allowable decrease for testing is 40. Reduction of 30 is within the allowable range. Therefore shadow price of 112.5 is applicable. Objective value would decrease by 30*112.5 = 3375

New objective value = 51750 - 3375 = $ 48,375

New optimal mix: Q = 37.5, B = 105

iii) Shadow price os testing is 112.5 Therefore, I would be willing to pay $ 112.5 for each extra hour of testing

iv) IT is a non-binding constraint. (shadow price is 0) Therefore, I would not be willing to pay anything for extra materials to build more boats. (the existing material for 110 boats is not fully utilized)