Question

A company, 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.

Answer 1

Part A Answer: C(x)= 750+50x

Part B Answer: x(t)= 50t

Part C Answer: C(x(t))= 750+300t

trust me, i did the algebra CFU ;)

oh and the person above or below has answers that are wrong but some of his steps are correct. he or she may have forgotten or mixed up the steps.

Answer 2

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.