The Clapton Company manufactures two products: Alpha and Beta.The costs and revenues are as follows: Total demand for Alpha is 10,000 units and for Beta is 6,000 units.Machine hours is a scarce resource.During the year,50,000 machine hours are available.Alpha requires 4 machine hours per unit,while Beta requires 2.5 machine hours per unit.
How many units of Alpha and Beta should Clapton produce?
A)a
B)b
C)c
D)d

Question

Quizplus · Accepted Answer

To maximize the profit, the company needs to produce the products that generate the highest contribution margin per machine hour.

Alpha:

Contribution margin per unit = $75 - $35 = $40
Machine hours per unit = 4
Contribution margin per machine hour = $10 ($40/4)

Beta:

Contribution margin per unit = $60 - $30 = $30
Machine hours per unit = 2.5
Contribution margin per machine hour = $12 ($30/2.5)

Therefore, the company should produce more units of Beta because it generates a higher contribution margin per machine hour. To determine the optimal production quantities, we need to calculate the total machine hours required for each product:

Alpha: 10,000 units x 4 machine hours per unit = 40,000 machine hours
Beta: 6,000 units x 2.5 machine hours per unit = 15,000 machine hours

The total machine hours required to produce all units of Alpha and Beta are 55,000 machine hours. Since only 50,000 machine hours are available, the company cannot produce all units.

To find the optimal production quantities, we need to use a linear programming model. The objective is to maximize the total contribution margin subject to the machine hour constraint and non-negativity constraints.

The optimal production quantities are:

Alpha: 8,333 units (40,000/4.8)
Beta: 6,000 units

The total contribution margin is:

(8,333 x $40) + (6,000 x $30) = $699,990

Therefore, the best choice is to produce 8,333 units of Alpha and 6,000 units of Beta to maximize the profit.

The Clapton Company Manufactures Two Products: Alpha and Beta