Rosie's Company has three products, P1, P2, and P3. The maximum Rosie's can sell is 82,000 units of P1, 75,000 units of P2, and 63,000 units of P3. Rosie's has limited production capacity of 60,000 hours. It can produce 12 units of P1, 6 units of P2, and 3 units of P3 per hour. Contribution margin per unit is $5.00 for the P1, $15.00 for the P2, and $25.00 for the P3. What is the most profitable sales mix for Rosie's Company?

P2 75,000 P3 63,000 P1 2,117

Explanation:

The computation of most profitable sales mix is shown below:-

Product P1 P2 P3

Contribution margin

per unit $5 $15 $25

Machine hour

per unit 0.08 0.17 0.33

For computing the machine hour per unit we simply divide 1 by Number of units produced per hour

Contribution margin

per hour $62.50 $88.23 $75.76

For computing the contribution margin per hour we divide contribution margin per unit by machine hour per unit

Ranking 2 1 3

A B C = A * B

Maximum units that Machine hour Machine hour

can be produced per unit Used

Product P2 75,000 0.17 12,750

Product P3 63,000 0.33 20,790

Total machine hours used 33,540

Total machine hours available 60,000

Total machine hours left to produce product P1 26,460

Machine hour per unit required

to produce product P1 0.08

no. of units produced of product P1 2,117

(26,460 * 0.08)

So, the most profitable sales mix is shown below:-

Product Mix

Product P1 2,117 1.51%

Product P2 75,000 53.53%

Product P3 63,000 44.96%

Total 140,117