1. ## Simple Worded Question

A shop is selling sandwiches.
The cost that is involved amounts to $50 plus$.80 per sandwich. If the manager charges $x for each sandwich, where x = 3.5 - 0.01n and n is the number of sandwiches. Firstly I'm having trouble finding the expression for the revenue and for costs as functions of n. Also I can't seem to work towards this part of the question either. Show that an expression for the profit$P made from selling n sandwiches is

P = 2.7n-0.01n^2-50

2. ## Word problem

Hello ollieman
Originally Posted by ollieman
A shop is selling sandwiches.
The cost that is involved amounts to $50 plus$.80 per sandwich. If the manager charges $x for each sandwich, where x = 3.5 - 0.01n and n is the number of sandwiches. Firstly I'm having trouble finding the expression for the revenue and for costs as functions of n. Also I can't seem to work towards this part of the question either. Show that an expression for the profit$P made from selling n sandwiches is

P = 2.7n-0.01n^2-50
After the one-off cost of $$\displaystyle 50, the cost per sandwich is$$\displaystyle 0.80$, so the cost of making$\displaystyle n $sandwiches is $$\displaystyle (50 + 0.80n). The revenue is the income per sandwich multiplied by the number of sandwiches =$$\displaystyle (3.5 - 0.01n)n$ = \displaystyle (3.5n - 0.01n^2)$. The profit is the amount by which the revenue exceeds the costs; in other words:$\displaystyle P = (3.5n - 0.01n^2) - (50+0.80n)\displaystyle = (3.5 - 0.8)n - 0.01n^2 - 50\displaystyle = 2.7n -0.01n^2 - 50\$