Answer:
1. What is the contribution margin per hour of machine time for each type of team shirts?
<em>Homerun = </em> $ 50
<em>Goalpost</em> = $30
2. What is the optimal mix of team shirts?
Homerun = 50,890
Goalpost = 3,822
3. What is the total contribution margin earned for the optimal mix?
Total contribution margin earned for the optimal mix = $311,780
Explanation:
<em>1. Contribution margin per hour of machine time for each type of team shirts</em>
<em><u>Homerun</u></em>
Contribution margin per hour of machine = $5 / (6/60)
= $ 50
<em><u>Goalpost</u></em>
Contribution margin per hour of machine = $15 / (30/60)
= $30
<em>2. Optimal mix of team shirts</em>
Determine if <em>machine time</em> is a limiting factor
<u>Demanded Hours</u>
Homerun 0.1 × 50,890 = 5,089
Goalpost 0.5 × 50,890 = 25445
Total Hours Demanded = 30,534
<u>Available Hours</u>
Available hours =1,000 hour × 7 machines
=7,000 hours
Demanded Hours > Available hours
Therefore <em>machine time</em> is a limiting factor
Determine Mix
<em>Rank the T-Shirts based on contribution margin per hour of machine time</em>
Position 1. Homerun = 5,089
Position 2. Goalpost = 1,911 (takes the remaining hours)
Number of T-Shirts (mix)
Homerun = 5,089 / 0.1 = 50,890
Goalpost = 1,911 / 0.5 = 3,822
<em>3. The total contribution margin earned for the optimal mix</em>
Homerun = 50,890 × $5 =254,450
Goalpost = 3,822 × $15 = 57,330
Total = 311,780
