- #1

Shakattack12

- 24

- 2

## Homework Statement

A manufacturer makes a batch of n items with the cost (in dollars) of each item being:

n

^{2}-6n+35.

The manufacturer sells the items for $50 each. How many items should be produced in each batch to maximise profit.

## Homework Equations

Cost = C(n) = n

^{2}-6n+35

Revenue = R(n) = 50n

## The Attempt at a Solution

Profit = 50n - (n

^{2}-6n+35)

= 56n - n

^{2}-35

dP/dn = 56 - 2n

let dP/dn = 0

0 = 56 - 2n

n = 28

After testing the nature I found it to be a maximum which is all good but the textbook says the answer is 5. Where did I go wrong?