A plant can manufacture 50 golf clubs per day at a total daily cost of $5193 and

Question

A plant can manufacture 50 golf clubs per day at a total daily cost of $5193 and 60 golf clubs per day for a total cost of $5893. (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 lessthanorequalto x lessthanorequalto 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. C. The fixed cost and cost per club sum to the y intercept. The slope is the ratio of the two costs.

Explanation / Answer

Solution

Part (A)

Let y = total daily cost of producing x golf club per day. Then, linearity => y = a + bx……(1)

’50 golf clubs per day at a total daily cost of 5193 => a + 50b = 5193. …… (2)

’60 golf clubs per day at a total daily cost of 5893 => a + 60b = 5893. . …… (3)

(3) - (2): 10b = 700 or b = 70…………………………………………………(4)

(4) in (2): a = 1693……………………………………………………………(5)

(4) and (5) in (1) gives: total daily cost of producing x golf club per day = 1693 + 70x ANSWER

Part (B)

The graph should cut y-axis at 1693 and against 200 on the x-axis, value of y-axis should be 15693. Graph (A) only satisfies these two conditions. ANSWER

Part (C)

y-intercept, a, represents the total daily cost when x = 0, i.e., when nothing is produced, which in accounting terminology, represents overheads. The ‘b’ which represents the slope shows the unit cost of production. Thus, the correct answer is OPTION (B) ANSWER

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