Answer:
a. 7 units is the break-even quantity.
b. $5499 is the profit from 430 units.
c. 17 units must be produced for a profit of $130.
I'm not sure if you've already done parts b. and c., but I showed you how to do them just in case you haven't or didn't know how to since the steps from a. can help you with b. and c.
Explanation:
a. The break-even quantity is the least amount of units one must sell to produce a quantity. You can find it one of two ways:
- Either by setting the profit, P(x), equal to 0 and solving for x,
- or by setting the equations for R(x) and C(x) equal to each other and solving for x.
Step 1: Find the equation for P(x), the profit: Because b. and c. require us to know the profit function, we can find it and use the first method of finding the break-even quantity:
The profit is the difference between revenue and cost as
P(x) = R(x) - C(x)
Thus, we can substitute 28x for R(x) and 15x + 91 for C(x) to find P(x):
P(x) = 28x - (15x + 91)
P(x) = 28x - 15x - 91
P(x) = 13x - 91
Thus, the profit is P(x) = 13x - 91.
Step 2: Set P(x) equal to 0 and solve for x to find the number of units they need to sell to break even:
Now we can set P(x) equal to 0 and solve for x to determine the number of units they need to sell to break even:
P(x) = 0
13x - 91 = 0
13x = 91
x = 7
Thus, the maker of the religious medals must sell at least 7 units to break even.
b. To find the profit from 430 units, we plug in 430 for x in the profit function and solve:
P(430) = 13(430) - 91
P(430) = 5590 - 91
P(430) = 5499
Thus, $5499 is the profit from 430 units.
c. We can find the number of units that must be produced for a profit of $130 by setting P(x) equal to 130 and solving for x:
130 = P(x)
130 = 13x - 91
221 = 13x
17 = x
Thus, 17 units must be produced for a profit of $130.