A shoe manufacturer determines that its monthly revenue, R(q)R(q)R, (, q, ), 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

$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?

Step-by-step 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

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step-by-step explanation:

the formula for the equation of a circle is (x – h)2+ (y – k)2 = r2, where (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle. if a circle is tangent to the x-axis at (3,0), this means it touches the x-axis at that point.