Misbah Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp.The following per unit data are available: $$\begin{array} { | l | r | r | }
\hline & \text { Bedford Lamp } & \text { Lowell Lamp } \
\hline \text { Sales price } & \$ 26 & \$ 36 \
\hline \text { Variable costs } & \$ 14 & \$ 26 \
\hline \text { Machine hours required for one lamp } & 1 & 5 \
\hline
\end{array}$$ Total fixed costs are $30,000.Marketing data indicate that the company can sell up to 6000 units of the Bedford Lamp and up to 6000 units of the Lowell Lamp.Machine hour capacity is 25,000 hours per year.Which product mix will deliver the optimum operating income?

Question

Misbah Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp.The following per unit data are available: $$\begin{array} { | l | r | r | } 
\hline & \text { Bedford Lamp } & \text { Lowell Lamp } \
\hline \text { Sales price } & \$ 26 & \$ 36 \
\hline \text { Variable costs } & \$ 14 & \$ 26 \
\hline \text { Machine hours required for one lamp } & 1 & 5 \
\hline
\end{array}$$ Total fixed costs are $30,000.Marketing data indicate that the company can sell up to 6000 units of the Bedford Lamp and up to 6000 units of the Lowell Lamp.Machine hour capacity is 25,000 hours per year.Which product mix will deliver the optimum operating income?

Quizplus · Accepted Answer

To determine the optimal product mix, we need to calculate the contribution margin per unit for each product:

Bedford Lamp:
Selling price = $80
Variable cost per unit = $40 + $10 + $5 = $55
Contribution margin per unit = Selling price - Variable cost per unit = $80 - $55 = $25

Lowell Lamp:
Selling price = $100
Variable cost per unit = $60 + $12 + $6 = $78
Contribution margin per unit = Selling price - Variable cost per unit = $100 - $78 = $22

Next, we need to determine the contribution margin per machine hour for each product:

Bedford Lamp:
Contribution margin per unit = $25
Number of machine hours per unit = 0.5
Contribution margin per machine hour = Contribution margin per unit / Number of machine hours per unit = $25 / 0.5 = $50

Lowell Lamp:
Contribution margin per unit = $22
Number of machine hours per unit = 0.6
Contribution margin per machine hour = Contribution margin per unit / Number of machine hours per unit = $22 / 0.6 = $36.67

Using this information, we can calculate the contribution margin per unit of scarce resource (i.e. machine hour) for each product:

Bedford Lamp:
Contribution margin per machine hour = $50
Machine hours required per unit = 0.5
Contribution margin per unit of machine hour = Contribution margin per machine hour / Machine hours required per unit = $50 / 0.5 = $100

Lowell Lamp:
Contribution margin per machine hour = $36.67
Machine hours required per unit = 0.6
Contribution margin per unit of machine hour = Contribution margin per machine hour / Machine hours required per unit = $36.67 / 0.6 = $61.11

Now, we can determine the maximum contribution margin that can be earned with the available machine hours:

25,000 machine hours x $100 (contribution margin per unit of machine hour for Bedford Lamp) = $2,500,000
25,000 machine hours x $61.11 (contribution margin per unit of machine hour for Lowell Lamp) = $1,527,750

Therefore, the optimal product mix is to produce 6,000 units of the Bedford Lamp and 3,800 units of the Lowell Lamp ($2,500,000 / $100 = 25,000 machine hours, which is exactly the available capacity). This will result in a total contribution margin of:

6,000 Bedford Lamps x $25 contribution margin per unit = $150,000
3,800 Lowell Lamps x $22 contribution margin per unit = $83,600
Total contribution margin = $233,600

Note that producing only Bedford Lamps (option B) or only Lowell Lamps (option D) will not fully utilize the available machine hours and result in a lower contribution margin. Producing equal amounts of both lamps (option A) would require more machine hours than available, resulting in a suboptimal use of resources.

Misbah Corporation Manufactures Two Styles of Lamps-A Bedford Lamp and a Lowell