Question

Nutmeg Corporation operates a manufacturing company with total available capacity per year of 300,000 minutes. Nutmeg produces two models of widgets, Premium and Superior. There is unlimited demand for each product. Information relating to the products is as follows: Premium Superior Contribution margin per unit $80 $84 Machine minutes needed per unit 10 12 If only one product can be produced, what is the largest possible total contribution margin that can be realized each period?

Answer 1

Concept to be applied is Limiting factor.

Facts of the question :

Only one product can be produced by Nutmeg corporation.

Demand for the both the products is unlimited.

Machine minutes capacity per year is 300,000 minutes.

Entity produces two models of gadgets - Premium and superior

Contribution margin per unit for premium is $80 per unit and for superior is $ 84 per unit

Machine minutes required per unit for Premium gadget is $ 10 and superior gadget is $ 12

Analysis:

Here the entity can manufacture any number of both the products since the demand is unlimited.

However , in the question it is clearly stated that the entity can manufacture only one product with the available machine minutes.

Now the question is which product to be selected in order to maximize the contribution margin and calculation of the same.

Limiting factor is nothing but a key or critical factor which has the ability to limit the production.

In the given case, machine minutes is the limiting factor becuase if we have unlimited machine minutes we can manufacture unlimited product gadgets and sell them as their demand is unlimited.

In case of limiting factor we have to rank the products to be produced based on the contribution margin per limiting factor and not on the basis of contribution margin per unit.

The reason for the same is if we are using the limiting factor for product which has less contribution but which requires less utilisation of the same limiting factor, the goods manufactured using the limiting factor can be more and thereby contribution margin can be earned more. However, even though the contribution margin for one product is high but it requires more utilisation of limiting factor, it will reduce the capacity of the goods that can be manufactured and therby contribution margin earned will be reduced.

Final answer:

The given case can be solved by calculating the contribution margin per machine minutes for each product and the entity should manufacure the product which has more contribution margin per machine unit to maximize the total contribution margin.

Calculation of contribution margin per machine minute = contribution margin per unit (/) No. Of machine minutes

By substituting the values given in question,

A) For premium gadget ,

Contribution margin per machine minutes

= $ 80 (/) 10

= $8

B) For superior gadet,

Contribution margin per machine minutes

= $ 84 (/) 12

= $ 7

Since the contribution margin per machine minute for premium gadget is higher (8 is greater than 7), the entity should utilise the available machine minutes of 300,000 to produce premium gadget .

Units of premium gadget that can be produced

= Total minutes (/) No. Of minutes per unit

= 300,000(/) 10

= 30,000 units of premium gadget can be produced.

Contribution margin per unit of premium gadget = $ 80 per unit

Thereby, Total contribution margin earned

= No. Of units produced * contribution per unit

= 30,000 * 8

= $240,000

Conclusion :

Premium gadget to be produced since  

the contribution margin per machine minute (limiting factor) is high for premium gadget and

The largest possible Total contribution margin that can be earned = $ 240,000.