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A plant can manufacture 50 golf clubs per day at a total daily cost of $4881 and 80 golf clubs per day for...

A plant can manufacture 50 golf clubs per day at a total daily cost of $4881 and 80 golf clubs per day for a total cost of $6831.
(A) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs.
(B) Graph the total daily cost for 0 ≤ x ≤ 200.
(C) Interpret the slope and y intercept of the cost equation.
(A) C =
(Simplify your answer. Use integers or fractions for any numbers in the expression. Do not include the $ symbol in your answer.)
(B) Choose the correct graph of the total daily cost below.
(C) Interpret the slope and y intercept. Choose the correct answer below
A. The y intercept is the cost per club and the slope is the fixed cost
B. The y intercept is the fixed cost and the slope is the cost per club

Answer

(A) To find the total daily cost, C, of producing x golf clubs, we use the formula for a line: C = mx + b. We have two points: (50, 4881) and (80, 6831). The slope m is calculated as follows:

m = (6831 - 4881) / (80 - 50) = 1950 / 30 = 65.

Using the point (50, 4881) to find b:

4881 = 65(50) + b => b = 4881 - 3250 = 1631.

Thus, the equation is C = 65x + 1631.

(B) The correct graph is the one that represents the line C = 65x + 1631 for 0 ≤ x ≤ 200. This corresponds to option C.

(C) The y intercept is the fixed cost and the slope is the cost per club. This corresponds to option B.

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