Question

The Academic T-Shirt Company did a cost study and found that it costs $1400 to produce 600 “I Love Math” T-shirts. The total cost is $1600 for a volume of 700 T-shirts.a. Determine the linear cost-volume function.b. What is the fixed cost?c. What is the unit cost?

Answer 1

Given

The Academic T-Shirt Company did a cost study and found that it costs $1400 to produce 600 “I Love Math” T-shirts. The total cost is $1600 for a volume of 700 T-shirts.

`\begin{gathered} (600,1400) \\ (700,1600) \end{gathered}`

We are going to find the slope

Where y is the cost

and x is the volume

`slope(m)=(y_2-y_1)/(x_2-x_1)=(1600-1400)/(700-600)=(200)/(100)=2`
`\begin{gathered} y-y_1=m(x-x_1) \\ y-1400=2(x-600) \\ y-1400=2x-1200 \\ collect\text{ the like terms} \\ y=2x-1200+1400 \\ y=2x+200 \end{gathered}`

The final answer