assume that the situation can be expressed as a linear cost function. find the cost function in this case…

assume that the situation can be expressed as a linear cost function. find the cost function in this case. marginal cost: $35; 150 items cost $7000 to produce. the linear cost function is c(x) =

assume that the situation can be expressed as a linear cost function. find the cost function in this case. marginal cost: $35; 150 items cost $7000 to produce. the linear cost function is c(x) =

Answer

Explanation:

Step1: Recall the form of linear cost function

The linear cost - function is $C(x)=mx + b$, where $m$ is the marginal cost and $b$ is the fixed cost. Given that the marginal cost $m = 35$. So, $C(x)=35x + b$.

Step2: Use the given data point to find $b$

We know that when $x = 150$, $C(150)=7000$. Substitute these values into the cost - function $C(x)=35x + b$. We get $7000=35\times150 + b$. First, calculate $35\times150=5250$. Then the equation becomes $7000 = 5250 + b$. To solve for $b$, subtract 5250 from both sides of the equation: $b=7000 - 5250=1750$.

Step3: Write the final cost function

Substitute $b = 1750$ into $C(x)=35x + b$. The cost function is $C(x)=35x + 1750$.

Answer:

$C(x)=35x + 1750$