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A company manufactures small refrigerators. The total cost to manufacture 160 refrigerators is
$17665. The total costs to manufacture 182 refrigerators is $19865. Assume that total cost, C, is
linearly related to the number of refrigerators, x, the company manufactures and includes a fixed
cost and a cost per refrigerator.

Write the cost function, C(x) in terms of x, the number of refrigerators manufactured.

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onyebuchinnaji

The cost function, C(x) in terms of x, the number of refrigerators manufactured is written as C(x) = 1665 + 100x

The given parameters;

  • total cost of manufacturing  160 refrigerators = $17665.
  • total cost of manufacturing  182 refrigerators = $19865.
  • total cost, C, is linearly related to the number of refrigerators, x

The linear equation is set up as follows;

C = b + ax

where;

  • b is the fixed cost
  • a is  cost per refrigerator

First equation;

17665 = b + 160a  -------(1)

Second equation;

19865 = b + 182a -----(2)

subtract equation 1 from equation 2 to solve for the value of a;

2200 = 22a

[tex]a = \frac{2200}{22} \\\\a = 100[/tex]

Solve for the value of b;

17665 = b + 160(100)

17665 = b + 16000

b = 17665 - 16000

b = 1665

C(x) = b + ax

C(x) = 1665 + 100x

Thus, the cost function, C(x) in terms of x, the number of refrigerators manufactured is written as C(x) = 1665 + 100x

Learn more here: https://brainly.com/question/13792039

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