Question

Connolly Company produces two types of lamps, classic and fancy, with unit contribution margins of $13 and $21, respectively. Each lamp must spend time on a special machine. The firm owns four machines that together provide 18,000 hours of machine time per year. The classic lamp requires 0.20 hours of machine time, the fancy lamp requires 0.50 hours of machine time.

How many of each type of lamp must be sold to optimize total contribution margin?

a. 90,000 classic lamps; 0 fancy lamps
b. 0 classic lamps; 9,000 fancy lamps
c. 18,000 classic lamps; 0 fancy lamps
d. 0 classic lamps; 30,000 fancy lamps
e. 10,000 classic lamps; 10,000 fancy lamps

Answer 1

a. 90,000 classic lamps; 0 fancy lamps

Step-by-step explanation:

To determine the optimise total contribution, we need to calculate the contribution margin per hour of machine time for both the lamps. Then the result of whichever is higher would be produced.

Moreover, as there is no limitation on how many lamps can be produced, therefore, we would assume that we can make as many as we want up to the limit of machine-hours available. The calculation is done as follows:

Contribution margin per hour of machine time for classic lamp = Contribution/machine hours to build one classic lamp

Contribution margin per hour of machine time for classic lamp = 13 / 0.2

Contribution margin per hour of machine time for classic lamp = 65

Contribution margin per hour of machine time for fancy lamp = Contribution/machine hours to build one fancy lamp

Contribution margin per hour of machine time for fancy lamp = 21 / 0.5

Contribution margin per hour of machine time for fancy lamp = 42

Since classic lamp has the higher contribution margin per hour. Therefore, all the machine hours would be used to make classic lamps.

= 18,000 / 0.2

= 90,000

Hence, 90,000 classic lamps would be sold while no fancy lamps will be sold to optimise total contribution (which would be 65 x 18,000 = $1,170,000).