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.

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Step-by-step 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

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