Answer:
i.
a. Break-even volume: 70,423 units;
b. Unit cost if 100,000 units are made: $31;
c. Annual profit at 100,000 units made: $420,000.
ii.
The company should make this garment if the company should be able to manufacture and sell 105,634 units per year.
Explanation:
i.
a. Break-even volume:
Denote x is the break-even volume, then we have:
1,000,000 = 0.4* X * ( 28 - 21) + 0.6 * X * ( 40 -21) <=> 14.2X = 1,000,000 <=> X = 70,423 units;
b. Unit cost if 100,000 units are made:
Total cost if 100,000 units are made = 1,000,000 + 100,000 * 21 = $3,100,000;
Unit cost = 3,100,000 / 100,000 = $31.
c. Annual profit at 100,000 units made = Total revenue - Total cost = 100,000*0.4*28 + 100,000*0.6*40 - 3,100,000 = 3,520,000 - 3,100,000 = $420,000.
ii.
To meets the minimum expected profit given costs, selling price and sell structure remains the same, the company should be able to manufacture and sell Y units per year, with Y is calculated as below:
0.4 * Y * (28-21) + 0.6 * Y * (40-21) - 1,000,000 = 500,000 <=> 14.2Y - 1,000,000 = 500,000 <=> 14.2Y = 1,500,000 <=> Y = 105,634 units
So, it should make this garment if the company should be able to manufacture and sell 105,634 units per year.
