Solve the equations in Parts A and B using inverse operations. Check your solutions. In your final answer, include all of your w
2 answers:
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Answer:
a) At break even point, Q = 380 units, Sales dollar = $5247.8
b) Margin of safety at Q = 400 units is 0.05 × 100 = 5
c) Number of cakes that need to be sold before a profit of $2200 is made = 595 cakes
Step-by-step explanation:
Let the number of units be Q
Cost equation = (fixed cost) + (Variable cost)
Fixed Cost = $3898.8
Variable Cost = Variable cost per unit × number of units produced = (2.32 + 1.11 + 0.12) × Q = 3.55Q
Cost equation = 3898.8 + 3.55Q
Revenue = price per unit × number of units sold = 13.81 × Q = 13.81Q
At break even point,
Total cost = Revenue
3898.8 + 3.55Q = 13.81Q
10.26Q = 3898.8
Q = 380 units
In sales dollars, R = 13.81Q = 13.81 × 380 = $5247.8
b) Margin of safety = 100 × (Current sales - Breakeven point sales)/(current sales)
Breakeven point sales = $5247.8
At Q = 400 units, Current sales = 13.81 × 400 = $5524
Margin of safety = 100 × (5524 - 5247.8)/5524 = 5
c) number of cakes that Cove must sell to generate $2,200 in profit.
Profit = Revenue - Total Cost
2200 = 13.81Q - (3898.8 + 3.55Q)
2200 = 10.26Q - 3898.8
10.26Q = 2200 + 3898.8 = 6098.8
Q = 594.4 = 595 units
