Irrigation improves the yield of strawberries per acre according to the function S = - (w-2) ^2 + 50 where S is the number of pints of strawberries grown per acre and w is the acre-feet of water used. Strawberries sell for $3 per pint and water costs $5 per acre-foot. Graph the yield function.

Given:

The yield of strawberries per acre is

S = - (w - 2) ² + 50

where

S = number of pints of strawberries per acre

w = acre-feet of water

Strawberries sell for $3 per pint

Water costs $5 per acre-feet.

The yield function is the revenue minus the expenses. It is

Y = (S pints) * ($3 per pint) - (w acre-ft) * ($5 per acre-ft)

Y = - 3 (w - 2) ² - 5w + 150 dollars

A graph of the yield function is shown below.

It indicates that

a) the yield is maximum when the acre-feet is about 1.5;

b) the yield increases between zero and 1.5 acre-feet;

c) the yield decreases quickly when the acre-feet exceed 1.5;

d) the yield vanishes when the acre-feet exceed 8.