Question

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.

Answer 1

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.