Answer:
<em>Since the profit is positive, Rebotar not only broke even, they had earnings.</em>
Step-by-step explanation:
<u>Function Modeling</u>
The costs, incomes, and profits of Rebotar Inc. can be modeled by means of the appropriate function according to known conditions of the market.
It's known their fixed costs are $3,450 and their variable costs are $12 per basketball produced and sold. Thus, the total cost of Rebotar is:
C(x) = 12x + 3,450
Where x is the number of basketballs sold.
It's also known each basketball is sold at $25, thus the revenue (income) function is:
R(x) = 25x
The profit function is the difference between the costs and revenue:
P(x) = 25x - (12x + 3,450)
Operating:
P(x) = 25x - 12x - 3,450
P(x) = 13x - 3,450
If x=300 basketballs are sold, the profits are:
P(300) = 13(300) - 3,450
P(300) = 3,900 - 3,450
P(300) = 450
Since the profit is positive, Rebotar not only broke even, they had earnings.
For this problem, we are given a quadratic equation that models the total amount spent on clothing and footwear in the years 2000-2009. We need to use the model to determine the maximum amount spent during the period.
The equation is shown below:
Since the leading term is negative, the vertex of this function will represent an absolute maximum value. Therefore we can determine the vertex to answer the problem, the vertex's coordinates are given below:
Then we have:
In the year 2008, 384 billion was spent on clothing and footwear.
A) y=55x+80
C) y=55(12)+80 = 740$ after a year
B)
