Answer:
$9500
Question:
A shoe manufacturer determines that its monthly revenue, R(q)=−0.31(q−260)^2 + 9500 in dollars, is given by the function defined above, where qqq is the number of pairs of shoes sold each month. What is the maximum value of the company's monthly revenue in dollars?
Explanation:
To determine the maximum value of the company's monthly revenue in dollars, we need to find the value of q such that we would have the highest value of R(q).
Given expression:
R(q) = −0.31 × (q−260)^2 + 9500
Let's determine the value of R(q) when q is less than 260; greater than 260; and equal to 260.
For example, if q = 100
R(q) = -0.31×(100-260)² + 9500 = $1564
If q = 300
R(q) = -0.31×(300-260)² + 9500 = $9004
If q = 260
R(q) = -0.31×(260-260)² + 9500 = $9500
From the above, R(q) = −0.31 × (q−260)^2 + 9500 would always have a lesser value when q is not equal 260.
Therefore, R(q) is at its maximum when q = 260.
R(260) = $9500
The maximum value of the company's monthly revenue in dollars = $9500