165k views
2 votes
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.

User Stan James
by
6.8k points

2 Answers

3 votes

Answer:

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.

User Chris McGrath
by
7.3k points
3 votes

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.


User Aag
by
7.7k points