Acompany, second brain, produces calculators. it costs them $750 operating cost per week plus $6 per case of calculators manufactured. they estimate that 50 cases of calculators are produced every hour. the plant typically runs calculator production for 10 hours a day. part a: write a function c(x) to represent the cost of production, c, for a week. part b: write a function x(t) to represent the amount of cases, x, produced in t hours. part c: write a function c(x(t)) that can be used to find the cost to produce calculators for a week.

A.

Operating cost = $750

Working hours per day = 10

Total working hours per week = 70

Number of cases produced per hour = 50

So, number of cases produced in a week = 50 × 70 = 3500

If x is the manufacturing cost per hour, then

Manufacturing cost for 3500 cases produced in a week = 3500x.

Total cost = Operating cost + Manufacturing cost

Hence, total cost C(x) = 750 + 3500x.

B.

Number of cases produced in 1 hour = 50

Number of cases produced in t hours = 50t.

Cost per case = $6.

Amount of cases produced in t hours x(t) = 6 × 50t = 300t.

C.

C(x(t)) = C(300t) = 750 + 300t.

1.5%

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