Answer
a. $c(x)=0.55x+525.00$
b. $p(x)=-0.001x^2+2.45x-525$
c. $p(x)=975.625$ at $x=1225$
Work Step by Step
a. The cost function is the sum of the fixed cost and the variable cost. Therefore, if the fixed cost is $525.00$ and the variable cost is $0.55$ for making a roast beef sandwich. for $x$ number for roasted beef sandwich made weekly, the weekly cost functions is $c(x)=0.55x+525.00$
b. The profit function is the difference between the revenue and the cost function, $p(x)=r(x)-c(x)=-0.001x^2+2.45x-525$
c. $x=-b/2a$, we can find the vertex of a parabola (the graph of the quadratic function), meaning we can find the maximum point if a parabola is downward opening parabola or the minimum point if a parabola is upward opening parabola. $p(x)=-0.001x^2+2.45x-525$, $x=-b/2a=-2.45/2(-0.001)=1225$. therefore, $p(1225)=975.625$ is the maximum weekly profit.
