Figure 13-3. Elegance Bath Products,Inc.(EBP)makes a variety of ceramic sinks and tubs.EBP has just developed a line of sinks and tubs made from a mixture of glass and ceramic.The sinks sell for $150 each and have variable costs of $80.The tubs sell for $600 and have variable costs of $450.The glass and ceramic sinks and tubs require the use of specialized molding equipment.The specialized molding equipment has 4,050 hours of capacity per year.A sink uses an average of 2 hours of specialized molding equipment time; a tub uses an average of 5 hours of specialized molding equipment time.
Refer to Figure 13-3.Assuming that specialized molding equipment time is the only constrained resource,and that EBP can sell as many tubs and sinks as it can produce,how many sinks should be sold?
A)2,050
B)2,025
C)zero
D)4,050
E)810

Question

Quizplus · Accepted Answer

To determine the number of sinks EBP should sell, we need to maximize the contribution margin earned from each sink. The contribution margin is the selling price minus the variable cost per unit.

For each sink, the contribution margin is:

Contribution margin per sink = Selling price - Variable cost per unit = $150 - $80 = $70

For each tub, the contribution margin is:

Contribution margin per tub = Selling price - Variable cost per unit = $600 - $450 = $150

However, we need to consider the limited capacity of the specialized molding equipment. Since a sink uses an average of 2 hours and a tub uses 5 hours of molding equipment time, we can set up the following constraint:

2 hours per sink x number of sinks + 5 hours per tub x number of tubs ≤ 4,050 hours of molding equipment capacity

Let's rearrange this equation to solve for the maximum number of sinks that can be produced:

2x + 5y ≤ 4,050

where x is the number of sinks and y is the number of tubs.

We can use trial and error to find the maximum number of sinks that satisfy this constraint. For example, if we produce 2,000 sinks and no tubs, we use:

2 x 2,000 + 5 x 0 = 4,000 hours of molding equipment capacity

This would leave 50 hours of molding equipment capacity unused. So, we can produce more sinks. If we produce 2,025 sinks and no tubs, we use:

2 x 2,025 + 5 x 0 = 4,050 hours of molding equipment capacity

This is the maximum number of sinks we can produce while fully utilizing the molding equipment capacity. Therefore, the best choice is B) 2,025 sinks.