A small bicycle manufacturer has daily fixed costs of 1950 a

A small bicycle manufacturer has daily fixed costs of $1950 and each bicycle costs $80 to manufacture. Let x represent the number of bicycles manufactured and C(x) represents the cost of manufacturing. Complete parts (a) through (c). Write a linear function that models this situation. C(x) = ____ Find C(6). Interpret your answer in the context of this problem. C(6) = ____. This means that the cost of manufacturing ____ bicycles in a day is $____. Find the value of x if C(x) = 2750. Express this situation using function notation, and interpret it in the context of this problem. x = ____ when C(x)=2750. This means that the cost of manufacturing _____ bicycles in a day is $ ____.

Solution

(a).If x bicycles are manufactured daily and if the daily fixed cost is $ 1950, then the daily fixed cost per bicycle is 1950/x. Further, since each bicycle costs $ 80 to manufacture, hence, the total daily cost is C(x) = 80+ 1950/x.

(b). On substituting x = 6, we get C(6) = 80 +1950/6 = 80+325 = $405.This means that the cost of manufacturing 6 bicycles in a day is $ 405. C(6) = $405.This means that the cost of manufacturing 6 bicycles in a day is $ 405.

(c ). If C(x) = 2750, then 80+ 1950/x = 2750 or,on adding -80 to both the sides, 1950/x = 2750-80 = 2670. Now, on multiplying both the sides by x, we get 2670x = 1950 so that x = 1950/2670 = 0.730337078. However, since x can only be a whole number, we have C(x) = 2750/0.730337078 = $ 3765.38 ( on rounding off to the nearest cent). x = 0.730337078 when C(x) = 2750. This means that the cost of manufacturing 1 bicycle in a day is $ $ 3765.38.