a company manufactures small refrigerators. the total weekly cost to manufacture 110 refrigerators is…

a company manufactures small refrigerators. the total weekly cost to manufacture 110 refrigerators is $10655. the total cost to manufacture 166 refrigerators during a week is $15695. 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 87 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 110 refrigerators is $10655. the total cost to manufacture 166 refrigerators during a week is $15695. 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 87 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 of the cost - function

The cost function is linear, of the form $C(x)=mx + b$. We have two points $(x_1,C(x_1))=(110,10655)$ and $(x_2,C(x_2))=(166,15695)$. The slope $m$ (the variable - cost per unit) is given by the formula $m=\frac{C(x_2)-C(x_1)}{x_2 - x_1}$. $m=\frac{15695 - 10655}{166 - 110}=\frac{5040}{56}=90$

Step2: Find the y - intercept (fixed cost)

We use the point - slope form $y - y_1=m(x - x_1)$ with the point $(110,10655)$ and $m = 90$. Substituting into $C(x)=mx + b$, we get $10655=90\times110 + b$. $10655=9900 + b$, so $b=10655 - 9900=755$.

Step3: Write the cost function

The cost function is $C(x)=90x + 755$.

Step4: Find the cost of manufacturing 87 refrigerators

Substitute $x = 87$ into $C(x)$: $C(87)=90\times87+755=7830 + 755=8585$.

Step5: Identify the fixed cost

The fixed cost is the y - intercept of the cost function. So the fixed cost is $b = 755$.

Step6: Identify the cost per additional refrigerator

The cost per additional refrigerator is the slope of the cost function. So it is $90$.

Answer:

A. $C(x)=90x + 755$ B. $8585$ C. $755$ D. $90$