Answer:
$302,500
Step-by-step explanation:
If cost (C) = $7, then Sales (S) = 37,500 units
If cost (C) = $15, then Sales (S) = 17,500 units
The slope of the linear relationship between units sold and cost is:
[tex]m=\frac{37,500-17,500}{7-15}\\m= -2,500[/tex]
The linear equation that describes this relationship is:
[tex]s-s_0 =m(c-c_0)\\s-17500 =-2500(c-15)\\s(c)=-2500c + 55,000[/tex]
The revenue function is given by:
[tex]R(c) = c*s(c)\\R(c)=-2500c^2 + 55,000c[/tex]
The cost at which the derivative of the revenue equals zero is the cost that yields the maximum revenue.
[tex]\frac{d(R(c))}{dc}=0 =-5000c + 55,000\\c=\$11[/tex]
The optimal cost is $11, therefore, the maximum revenue is:
[tex]R(11)=-2500*11^2 + 55,000*11\\R(11)=\$ 302,500[/tex]
