Answer:
The answer is below
Explanation:
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.
Solution:
A) Let us assume x cases are made per week. the cost of production is the sum of the operating cost and the cost of producing x amount of cases, hence:
C(x) = 750 + 6x
B) Since 50 cases are produced in an hour, the amount of cases produced in t hours is:
x(t) = 50 cases/hour * t hour
x(t) = 50t
C) If the company works for t hours in a week, the cost of production is:
C[x(t)] = 750 + 6(50t)
C[x(t)] = 750 + 300t