Questions: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed cost is 100; 70 items cost 2,200 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.
Fixed cost is 100; 70 items cost 2,200 to produce.

The linear cost function is C(x)=

Transcript text: Assume that the situation can be expressed as a linear cost function. Find the cost function. Fixed cost is $\$ 100 ; 70$ items cost $\$ 2,200$ to produce. The linear cost function is $C(x)=$ $\square$

Solution

Solution Steps

Step 1: Identify the Fixed Cost (b)

The fixed cost (b) is given as: $100.

Step 2: Determine the Variable Cost per Item (m)

Using the formula $m = \frac{C(x_2) - C(x_1)}{x_2 - x_1}$, where $C(x_1) = 2200$, $x_1 = 70$, $C(x_2) = 0$, and $x_2 = 0$, we calculate $m = \frac{0 - 2200}{0 - 70} = 31.43$.

Step 3: Write the Complete Linear Cost Function

Substituting $m = 31.43$ and $b = 100$ into $C(x) = mx + b$, we get the linear cost function: C(x) = 31.43x + 100.