A property developer is planning to build houses on 4 acres of land. She estimates that if she builds 16 houses, the profit per house will be $400,000, and that each additional house she builds will reduce her profit per house by$10,000. The total profit P(n), in thousands of dollars, from making n houses, can be modelled by the function:

Code:
P(n)= 560n-10n^2

(a) How much profit will the developer make from making 9 houses according to this
model?
$4, 230, 000 (b) Find the roots of the equation P(n) = 0, and use these to find how many houses the developer should build for maximum profit. State the value of this profit. The roots are when n = 0 or 56 build 28 houses for maximum profit$7,840,000 is the value of the profit if the developer builds 28 houses

(c) What is a sensible practical domain for P(n)?
starts with n = 0 – can’t have negative number of houses and ends with n= 28 – as this is the maximum value of P(n), after this the profit starts decreasing.
Code:
0<= n <= 28
(d) The developer needs to make at least $6,800,000 (i.e.$6800 thousand) to invest in a block of land she wishes to purchase for her next development project. Find algebraically the roots of the equation P(n) = 6800, and use your answer to suggest how many houses she needs to build to gain this much profit.

Code:
 560n-10n^2 -6800 = 0

n = 17.80196097 or 38.19803903

She should build 38 houses to make at least $6,800,000 I'm sorry I didn't include my working, but its quiet difficult to type it all out. Any assistance with this would be great, thanks for looking 2. (d) The developer needs to make at least$6,800,000 (i.e. $6800 thousand) to invest in a block of land she wishes to purchase for her next development project. Find algebraically the roots of the equation P(n) = 6800, and use your answer to suggest how many houses she needs to build to gain this much profit. Code: 560n-10n^2 -6800 = 0 n = 17.80196097 or 38.19803903 She should build 38 houses to make at least$6,800,000
if i get this right.. to make at least $6,800,000 she should build at least 18 houses, but not more than 38. 17 < houses built < 39 => at least$6,800,000

other answers are correct.

3. ## Thanks metlx

Hey metlx,

Thanks for your response! I've use the thank you button on you