Question

You are setting up a part-time business with an initial investment of $12,000. The unit cost of the product is $11.50, and the selling price is $19.00.Required:a. Find equations for the total cost C (in dollars) and total revenue R (in dollars) for x units.b. Find the break-even point by finding the point of intersection of the cost and revenue equations units.c. How many units would yield a profit of $1000?

Answer 1

Given Initial investment = $12,000

Cost per unit = $11.50

Selling price per unit = $19

a. For x unit

Total cost = Initial investment + Cost per unit * no of unit

= 12,000 + 11.50(x)

c(x) = 12,000 + 11.50(x)

R(x) = Selling price per unit * no of items

R(x) = 19 * x

R(x) = 19x

b. Break even point = R(x) = C(x)

19x = 12,000 + 11.50x

19x - 11.5x = 12,000

7.5x = 12,000

x = 12,000 / 7.5

x = 1600

So, break even point x = 1,600

c. For Profit = $1,000

P(x) = 1,000

P(x) = R(x) - C(x)

1000 = 19x - (12,000 + 11.5x)

1000 =19x - 11.5x - 12000

7.5x = 12000 + 1000

7.5x = 13000

x = 13000/7.5

x = 1733.33

So x = 1733 units

Hence, 1733 units will yield for $1,000 profit