Questions: A grocery store buys cereal using the cost function c(n)= when n<100 2n 100 ≤ n ≤ 500 1.9n when n>500 1.8n Where n is the number of boxes of cereal the grocery store buys and c(n) is the cost of the cereal. The grocery store then sells the cereal using the sales function s(c)=1.3c. What is the cost of the cereal if the grocery store buys 250 boxes?

A grocery store buys cereal using the cost function
c(n)= when n<100 2n 100 ≤ n ≤ 500 1.9n when n>500 1.8n
Where n is the number of boxes of cereal the grocery store buys and c(n) is the cost of the cereal. The grocery store then sells the cereal using the sales function s(c)=1.3c. What is the cost of the cereal if the grocery store buys 250 boxes?

Transcript text: A grocery store buys cereal using the cost function \[ \begin{array}{l} c(n)=\left\{\begin{array}{l} \text { when } n<100 \\ 2 n \end{array} \begin{array}{r} 100 \leq n \leq 500 \\ 1.9 n \\ 1.8 n \end{array} \begin{array}{l} \text { when } n>500 \end{array}\right. \end{array} \] Where $n$ is the number of boxes of cereal the grocery store buys and $c(n)$ is the cost of the cereal. The grocery store then sells the cereal using the sales function $\mathrm{s}(\mathrm{c})=1.3 \mathrm{c}$. What is the cost of the cereal if the grocery store buys 250 boxes?

Solution

Solution Steps

Step 1: Determine the Appropriate Cost Function

The cost function $ c(n) $ is defined in piecewise form based on the number of boxes $ n $. We need to determine which part of the piecewise function applies when the grocery store buys 250 boxes.