Question

Smash Company has 4 comma 000 machine hours available annually to manufacture badminton racquets. The following information is available for the two different racquets produced by​ Smash: Pro Unit sales price $ 500 Unit variable costs $ 125 Annual demand 2 comma 000 units Machine time 1 hours per unit Mid Unit sales price $ 125 Unit variable costs $ 80 Annual demand 6 comma 000 units Machine time 4 hours per unit How many units of each racquet should be manufactured for the company to maximize its operating​ income? (Round your answer to the nearest whole​ unit.)

Answer 1

Answer:

Pro = 2,000 units

Mid = 500 units

Explanation:

Step 1 Establish if we have a limiting factor in Production

Smash Company has 4,000 Machine Hours Available

Demand of Machine Hours:

Pro ( 2,000× 1 hr per unit)     = 2,000 hrs

Mid ( 6,000× 4hrs per unit)   = 24,000 hrs

Total                                        = 26,000 hrs

Machine Hours Required > Available Machine Hour

Therefore Machine Hours are a limiting factor !!

Step 2 Calculate the Contribution per unit of  limiting factor (machine hours) for each unit

Pro

Contribution = Sales-Variable Costs

                      = $ 500 - $ 125

                      = $ 375

Contribution per unit of limiting factor = Contribution per Unit / limiting factor required per unit

                                                                    = $ 375/ 1 hours

                                                                   =  $375

Mid

Contribution = Sales-Variable Costs

                      = $ 125 - $ 80

                      = $ 45

Contribution per unit of limiting factor = Contribution per Unit / limiting factor required per unit

                                                                    = $ 45 / 4 hours

                                                                   =  $ 11.25

Step 3 Rank the Products

1-Pro

2-Mid

Step 4 Determine mix

Utilization of Hours Available

Pro                                = 2,000 hrs

Mid (4,000 - 2,000)    = 2,000 hrs

Total Available Hours = 4,000 hrs

Product Mix is therefore :

Pro 2,000 /1 = 2,000

Mid 2,000 / 4 = 500