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 $$50$, the cost per sandwich is$ $0.80$, so the cost of making $n$ sandwiches is $$(50 + 0.80n)$. The revenue is the income per sandwich multiplied by the number of sandwiches =$ $(3.5 - 0.01n)n$ = \$ $(3.5n - 0.01n^2)$.

The profit is the amount by which the revenue exceeds the costs; in other words:

$P = (3.5n - 0.01n^2) - (50+0.80n)$

$= (3.5 - 0.8)n - 0.01n^2 - 50$

$= 2.7n -0.01n^2 - 50$