ANSWER
The marginal cost for producing 55 golf clubs is $31
STEP-BY-STEP EXPLANATION:
Given information
[tex]The\text{ total cost }in\text{ dollars = }550\text{ + 130x - }0.9x^2[/tex]
The next step is to find the marginal cost
The formula for finding marginal cost is given below as
[tex]MC\text{ = }\frac{\text{ }\Delta C}{\text{ }\Delta x}[/tex]
To find the marginal cost, we need to differentiate the total cost with respect to x
[tex]\begin{gathered} MC\text{ = }\frac{\text{ }\Delta C}{\text{ }\Delta x}\text{ = C'(x)} \\ C^{\prime}(x)\text{ = 0 + 1 }\times130x^{1\text{ - 1}}-2(0.9)x^{2\text{ -1}} \\ C^{\prime}(x)\text{ = 0 + 130 - 1.8x} \end{gathered}[/tex]
Therefore, the marginal cost is
[tex]C^{\prime}(x)\text{ = 130 - 1.8x}[/tex]
Part b
Find the marginal cost of producing 55 golf clubs
Let x = 55
The next step is to substitute the value of x = 55 into the above marginal cost formula
[tex]\begin{gathered} C^{\prime}(x)\text{ = 130 - 1.8x} \\ C^{\prime}(55)\text{ = 130 - 1.8(55)} \\ C^{\prime}(55)\text{ = 1}30\text{ - 99} \\ C^{\prime}(55)\text{ = \$31} \end{gathered}[/tex]
Therefore, the marginal cost for producing 55 golf clubs is $31
