Assume that the situation can be expressed as a linear cost function. Find the cost function in this case. Marginal​ cost: ​$40​; 180 items cost ​$9500 to produce. The linear cost function is ​C(x) = ____.

Accepted Solution

Answer:The linear cost function is [tex]C(x)=40\cdot x+2300[/tex]Step-by-step explanation:A linear cost function expresses cost as linear function of the number of items[tex]C(x)=mx+b[/tex]Here, C(x) is the total cost, and x is the number of items. The slope m is called the marginal cost and b is called the fixed cost.From the information given we knowm = $40 and C(180) = $9500We can find the value of b in this way[tex]C(x)=mx+b\\C(180)=\$40\cdot 180+b=\$9500[/tex]solving for b[tex]b=\$9500-\$40\cdot 180=\$2300[/tex]The linear cost function is [tex]C(x)=40\cdot x+2300[/tex]