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Assume a fixed cost of \(900, a variable cost of \)4.50, and a selling price of \(5.50.

a.What is the break-even point?

b.How many units must be sold to make a profit of \)500.00?

c.How many units must be sold to average \(0.25 profit per unit? \)0.50 profit per unit?$1.50 profit per unit?

Short Answer

Expert verified

a. The break-even point is $900.

b. To make a profit of $500, 1400units of output must be sold.

c. To make an average profit of $0.25 per unit, 1200units must be sold. For an average profit of $0.50 per unit,1800 units must be sold. An average profit of $1.50 per unit can’t be made.

Step by step solution

01

 Step 1:Average Profit 

Average profit is the profit earned per unit of output sold. It is calculated as total revenue earned from sales divided by the total output units sold in the market.

02

Calculating break-even point:

The break-even point will be equal to:

= 900/(5.5-4.5) = 900/1 = $900

03

Calculating profit:

Assuming x to be the unit of output sold. the profit function will be: (5.5 – 4.5)x - 900

The profit of $500 will be earned when:

=> x - $900 = $500

=> x = $1400

04

Calculating average profit per unit:

To know the average profit per unit. the profit is to be divided by the total output units sold, i.e. (x – 900)/x

To earn an average profit of $0.25 per unit, the output unit to be sold will be:

=>(x – 900)/x = 0.25

=> x = 1200 units

For an average profit of $0.50 per unit the required output sale will be:

=> (x – 900)/x = 0.5

=> x = $1800 units

Earning an average profit of $1.5 per unit the required sale would be:

=> (x – 900)/x = 1.5

=> x = -1800 units

Thus, earning an average profit of $0.25 and $0.5 requires the sale of 1200 and 1800 units, respectively. But earning an average profit of $1.5 is not possible.

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