Respuesta :
It should be noted that maximum value of the company's monthly revenue is $9500.
- From the information given, the shoe manufacturer determines that its monthly revenue, R(q)=−0.31(q−260)² + 9500
- It should be noted that the negative value won't be taken into consideration. Therefore, the revenue will be $9500.
Therefore, the maximum value of the company's monthly revenue in dollars will be $9500.
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The maximum value of the company's monthly revenue is $9500.
Given to us,
shoe manufacturer monthly revenue = [tex]R(q)=-0.31(q-260)^2+9500[/tex]
where, q is the number of pairs of shoes sold each month,
To maximize the value of the company's monthly revenue, we need to differentitae the function,[tex]R(q)=-0.31(q-260)^2+9500\\[/tex],
After diffrentiating it for the first time we get,
[tex]R(q)=-2\times0.31(q-260)[/tex]
equating it against 0,
we get, q = 260,
Equating the value of q into the function we will get $9500.
Therefore, the maximum value of the company's monthly revenue is $9500, this happened because -0.31(q-260)² is negative we need to remove that value to get the maximum value.
Hence, the maximum value of the company's monthly revenue is $9500.
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