Respuesta :
Given:
Fixed cost = b = $ 42,500
Production cost (Variable cost) /unit = m = $ 6/ unit
Let 'x' represent the number of unit, therefore the variable cost will be
[tex]6x[/tex]a) The cost function will be the sum of the fixed cost and the variable cost.
[tex]C(x)=6x+42500[/tex]b) The revenue function is the amount the product is sold per unit.
Recall: 'x' represents the number of units.
Therefore,
[tex]11\times x=11x[/tex]Hence, the revenue function R(x) is
[tex]R(x)=11x[/tex]c) The profit function is the difference between the revenue function and the cost function.
[tex]P\mleft(x\mright)=11x-\mleft(425000+6x\mright)=5x-42500[/tex]Hence, the profit function is
[tex]P\mleft(x\mright)=5x-42500[/tex]d) Let us compute the profit (loss) values when the units are 6000 and 11000
Using the profit function
[tex]P(x)=5x-42500[/tex]Therefore,
[tex]\begin{gathered} P(6000)=5(6000)-42500=30000-42500=-\text{ \$12500} \\ P(11000)=5(11000)-42500=55000-42500=\text{ \$12500} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} P(6000)=-\text{ \$12500 (which is a loss)} \\ P(11000)=\text{ \$12500 (this is a profit)} \end{gathered}[/tex]