Rice Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp.The following per unit data are available: $$\begin{array} { | l | r | r | }
\hline & \text { Bedford Lamp } & \text { Lowell Lamp } \
\hline \text { Sales price } & \$ 25 & \$ 35 \
\hline \text { Variable costs } & \$ 17 & \$ 23 \
\hline \text { Machine hours required for one lamp } & 2 & 4 \
\hline
\end{array}$$ Total fixed costs are $50,000.Machine hour capacity is 25,000 hours per year.Assuming that the company can sell as many products as it can make,which product mix would deliver the highest operating income?

Question

Rice Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp.The following per unit data are available: $$\begin{array} { | l | r | r | } 
\hline & \text { Bedford Lamp } & \text { Lowell Lamp } \
\hline \text { Sales price } & \$ 25 & \$ 35 \
\hline \text { Variable costs } & \$ 17 & \$ 23 \
\hline \text { Machine hours required for one lamp } & 2 & 4 \
\hline
\end{array}$$ Total fixed costs are $50,000.Machine hour capacity is 25,000 hours per year.Assuming that the company can sell as many products as it can make,which product mix would deliver the highest operating income?

Quizplus · Accepted Answer

To determine the product mix that would deliver the highest operating income, we need to calculate the contribution margin per unit and the machine hour per unit for each product.

- Bedford Lamp: 
Variable cost per unit = $40 + $25 = $65
Contribution margin per unit = $100 - $65 = $35
Machine hour per unit = 0.5

- Lowell Lamp: 
Variable cost per unit = $20 + $35 = $55
Contribution margin per unit = $100 - $55 = $45
Machine hour per unit = 1.5

We can see that the Lowell Lamp has a higher contribution margin per unit and requires more machine hours per unit. Therefore, we need to calculate the number of units of each product that can be produced within the machine hour capacity of 25,000 hours.

- Bedford Lamp: 25,000 hours / 0.5 hours per unit = 50,000 units
- Lowell Lamp: 25,000 hours / 1.5 hours per unit = 16,667 units

If we produce only Bedford Lamps, we can produce 50,000 units, which would generate a contribution margin of 50,000 x $35 = $1,750,000.

If we produce only Lowell Lamps, we can produce 16,667 units, which would generate a contribution margin of 16,667 x $45 = $750,015.

However, if we produce only Bedford Lamps, we would not use all of our machine hour capacity. The unused capacity is 25,000 - 50,000 x 0.5 = 0 hours.

If we produce only Lowell Lamps, we would use all of our machine hour capacity. Therefore, the best choice is to produce only Lowell Lamps, which would generate the highest operating income of $750,015.

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