a company manufactures small refrigerators. the total weekly cost to manufacture 134 refrigerators is…

a company manufactures small refrigerators. the total weekly cost to manufacture 134 refrigerators is $16755. the total cost to manufacture 149 refrigerators during a week is $18480. assume that the total weekly cost, c, is linearly related to the number of refrigerators, x, the company manufactures that week.\na) write the weekly cost function, c(x) in terms of x, the number of refrigerators manufactured.\nb) the total weekly cost to manufacture 77 refrigerators is $ \nc) the weekly fixed costs are $ \nnote: \fixed costs\ refer to costs that a manufacturer incurs even if they do not produce anything.\nd) each time an additional refrigerator is produced, the total weekly cost increases by $ \nquestion help: message instructor

a company manufactures small refrigerators. the total weekly cost to manufacture 134 refrigerators is $16755. the total cost to manufacture 149 refrigerators during a week is $18480. assume that the total weekly cost, c, is linearly related to the number of refrigerators, x, the company manufactures that week.\na) write the weekly cost function, c(x) in terms of x, the number of refrigerators manufactured.\nb) the total weekly cost to manufacture 77 refrigerators is $ \nc) the weekly fixed costs are $ \nnote: \fixed costs\ refer to costs that a manufacturer incurs even if they do not produce anything.\nd) each time an additional refrigerator is produced, the total weekly cost increases by $ \nquestion help: message instructor

Answer

Explanation:

Step1: Find the slope (variable - cost per unit)

The slope $m$ of the linear function $C(x)=mx + b$ is given by the formula $m=\frac{\Delta C}{\Delta x}$. We have two points $(x_1,C_1)=(134,16755)$ and $(x_2,C_2)=(149,18480)$. Then $m=\frac{18480 - 16755}{149 - 134}=\frac{1725}{15}=115$.

Step2: Find the y - intercept (fixed cost)

We use the point - slope form $C - C_1=m(x - x_1)$ with the point $(x_1,C_1)=(134,16755)$ and $m = 115$. So $C-16755=115(x - 134)$. Expand the right - hand side: $C-16755=115x-15410$. Then $C(x)=115x + 1345$. The fixed cost $b = 1345$.

Step3: Calculate cost for 77 refrigerators

Substitute $x = 77$ into $C(x)=115x + 1345$. Then $C(77)=115\times77+1345=8855 + 1345=10200$.

Step4: Identify fixed cost and variable cost increase

The fixed cost is the value of $b$ in the cost function $C(x)=115x + 1345$, which is 1345. The coefficient of $x$ is the increase in cost per additional unit, which is 115.

Answer:

A) $C(x)=115x + 1345$ B) $10200$ C) $1345$ D) $115$