Billings Company produces two products, Product Reno and Product Tahoe. Each product goes through its own assembly and finishing departments. However, both of them must go through the painting department. The painting department has capacity of 1,968 hours per year. Product Reno has a unit contribution margin of $96 and requires four hours of painting department time. Product Tahoe has a unit contribution margin of $78 and requires three hours of painting department time. There are no other constraints. Assume that only 500 units of each product can be sold. Required:1. What is the optimal mix of products? If required, round your answers to the nearest whole number. Optimal MixReno unitsTahoe units2. What is the total contribution margin earned for the optimal mix?$

Optimal product mix :Tahoe = 500 units, Renoe = 117 units

Total contribution = $50,232

Explanation:

When a business is faced with a problem of shortage of a resource which can be used to produced more than one product type, to maximize the use of the resource , the business should allocate the scare resource for production purpose in such a way that it maximizes the contribution per unit of the scare resource.

Therefore Billing Company should allocate the painting hours to maximise the contribution per unit of painting hour

Product                              Reno                   Tahoe

                                               $                          $

Contribution per unit               96                       78

Painting hour                            4                           3

Contribution per hour  *           24                         26

* = contribution per unit/painting hour per unit

Production mix

Product                      Unit              Painting hour

Tahoe                          500                   1500

Renoe                          117***                   468**                  

Total

**Balance of painting hour = 1968-1500= 468 hours

*** Unit of Renoe = 468/4=117 units

Optimal product mix = Tahoe = 500 units, Renoe = 117 units

Total contribution = (117× 96) +    (500×78)  = $50,232

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