2. [25] Most textbooks derive breakeven in terms of only linear functions of Tot

Question

2. [25] Most textbooks derive breakeven in terms of only linear functions of Total Cost and Total Revenue. In this case Total Cost is Fixed Cost plus Variable Cost per Unit times Demand. Total Revenue is Sales Price times Demand. Further, Profit is Total Revenue minus Total Cost. Develop an expression for the required Demand to exceed the Breakeven Point and make a specific value of Profit. 3. [25] Using linear functions of Total Cost and Total Revenue, find the Demand required to make $50,000 profit where Fixed Cost is $75,000, Sales Price is $15 per unit, and Variable Cost per Unit is $8

Explanation / Answer

2) Profit = Total revenue - Total cost

= Price x quantity (demand in the question) - (Fixed cost + Variable cost x quantity)

= PQ - F - VQ

= (P - V)Q - F

This is the required expression for the profit. Now when there is a positive profit so that the quantity is greater than break even we have

Profit > 0

(P - V)Q - F < 0

(P - V)Q > F

Q > F/(P - V)

This is the demand that exceeds breakeven point

3) Use the same process

(P - V)Q - F = 50000

(15 - 8)Q - 75000 = 50000

Q = 125000/7 = 17857.14

Hence the required demand is 17857.14 units

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