Clay Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp. The following per unit data are available: $$\begin{array} { | l | r | r | }
\hline & \text { Bedford Lamp } & \text { Lowell Lamp } \
\hline \text { Sale price } & \$ 25 & \$ 35 \
\hline \text { Variable costs } & \$ 17 & \$ 23 \
\hline \text { Machine hours required for 1 lamp } & 2 & 4 \
\hline
\end{array}$$ Total fixed costs are $30,000. Marketing data indicate that the company can sell up to 8,000 units of the Bedford lamp and up to 4,000 units of the Lowell lamp. Machine hour capacity is 25,000 hours per year. What product mix will deliver the optimum operating income?

Question

Clay Corporation manufactures two styles of lamps-a Bedford Lamp and a Lowell Lamp. The following per unit data are available: $$\begin{array} { | l | r | r | } 
\hline & \text { Bedford Lamp } & \text { Lowell Lamp } \
\hline \text { Sale price } & \$ 25 & \$ 35 \
\hline \text { Variable costs } & \$ 17 & \$ 23 \
\hline \text { Machine hours required for 1 lamp } & 2 & 4 \
\hline
\end{array}$$ Total fixed costs are $30,000. Marketing data indicate that the company can sell up to 8,000 units of the Bedford lamp and up to 4,000 units of the Lowell lamp. Machine hour capacity is 25,000 hours per year. What product mix will deliver the optimum operating income?

Quizplus · Accepted Answer

To determine the optimum product mix, we need to calculate the contribution margin per machine hour for each lamp:

- Bedford Lamp: $25 - $17 = $8 contribution margin per unit
- Lowell Lamp: $35 - $23 = $12 contribution margin per unit

We also need to calculate the machine hour requirements and contribution margin per machine hour for each lamp:

- Bedford Lamp: 2 machine hours per unit, $4 contribution margin per machine hour ($8 CM / 2 machine hours)
- Lowell Lamp: 4 machine hours per unit, $3 contribution margin per machine hour ($12 CM / 4 machine hours)

Since machine hour capacity is limited to 25,000 hours per year, we can set up the following constraints:

- 2 machine hours per Bedford Lamp and x Bedford Lamps ≤ 25,000 machine hours
- 4 machine hours per Lowell Lamp and y Lowell Lamps ≤ 25,000 machine hours

We also need to consider the market demand constraints:

- x Bedford Lamps ≤ 8,000 lamps
- y Lowell Lamps ≤ 4,000 lamps

The objective is to maximize operating income, which is equal to total contribution margin minus fixed costs. In equation form:

- Maximize Z = 8x + 12y - $30,000
- Subject to:
2x + 4y ≤ 25,000
x ≤ 8,000
y ≤ 4,000
x ≥ 0, y ≥ 0

Using linear programming software or a graphing calculator, we can solve this problem and find the optimal solution:

- x = 8,000 Bedford Lamps
- y = 2,250 Lowell Lamps
- Z = $62,000

Therefore, the best choice is C: 8,000 Bedford lamps, 2,250 Lowell lamps, which will deliver the maximum operating income of $62,000.

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