The cost in dollars to produce x youth baseball caps is C(x) = 4.3x + 75. The revenue in dollars from sales of x caps is R(x) = 25x. (a) Write and simplify a function P that gives profit in terms of x. (b) Find the profit if 50 caps are produced and sold.

Question
Algebra foundations
asked 2021-03-02
The cost in dollars to produce x youth baseball caps is C(x) = 4.3x + 75. The revenue in dollars from sales of x caps is \(\displaystyle{R}{\left({x}\right)}={25}{x}\).
(a) Write and simplify a function P that gives profit in terms of x.
(b) Find the profit if 50 caps are produced and sold.

Answers (1)

2021-03-03
(a)The profit is the revenue minus cost so we write:
\(\displaystyle{P}{\left({x}\right)}={R}{\left({x}\right)}−{C}{\left({x}\right)}\)
\(\displaystyle{P}{\left({x}\right)}={25}{x}−{\left({4.3}{x}+{75}\right)}\)
\(\displaystyle{P}{\left({x}\right)}={25}{x}−{4.3}{x}−{75}\)
\(\displaystyle{P}{\left({x}\right)}={20.7}{x}−{75}\)
(b)Using the profit function from (a), substitute x=50 for 50 caps:
\(\displaystyle{P}{\left({50}\right)}={20.7}{\left({50}\right)}−{75}\)
\(\displaystyle{P}{\left({50}\right)}={1035}−{75}\)
\(\displaystyle{P}{\left({50}\right)}={960}\rightarrow\${960}\)
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