Answer:
A. The function to express the cost is:
C(X) = $11.3*X + $27,000
The function to express the revenue is:
R(X) = $18.8*X
B. The break-even point is obtained for 3600 units
C. It is needed 3734 units to yield a profit of $1,000.
Explanation:
The expression for the cost of bussines is obtained by adding the initial investment to the cost of production of X units:
C(X) = $11.3*X + $27,000
Meanwhile the revenue for selling X is units is represented as:
R(X) = $18.8*X
Then the break-even point is found by equalling C(X) with R(X):
R(X) = C(X)
$18.8*X = $11.3*X + $27,000
$18.8*X - $11.3*X = $27,000
$ 7.5*X = $27,000
X = $27,000 / $7.5
X = 3,600 units
The profit of the bussines P(X) can be expressed sustracting the cost C(X) to the revenue R(X):
P(X) = R(X) - C(X)
P(X) = $18.8 * X - ($11.3*X + $27,000)
Equalling the profit to $1000 we will find the amount of units for selling:
$1,000 = $18.8*X - ($11.3*X + $27,000)
$1,000 = $18.8*X - $11.3*X - $27,000
$1,000 = $7.5*X - $27,000
$1,000 + $27,000 = $7.5*X
$28,000 = $7.5*X
$28,000 / $7.5 = X
X = 3734 units
