Suppose the equation for supply of water is Q_(s)=75+25P and the equation for demand for water looks like Q_(d)=147-20P where P is the price of a gallon and Q is the number of gallons. Determine the shortage from the price ceiling if the government sets the maximum price of water as 1.40 per gallon. Write the exact answer. Do not round.

To determine the shortage from the price ceiling, we need to calculate the quantity supplied and the quantity demanded at the government-set price of \$1.40 per gallon.<br /><br />First, substitute \( P = 1.40 \) into the supply equation:<br /><br />\[ Q_s = 75 + 25P \]<br />\[ Q_s = 75 + 25(1.40) \]<br />\[ Q_s = 75 + 35 \]<br />\[ Q_s = 110 \]<br /><br />Next, substitute \( P = 1.40 \) into the demand equation:<br /><br />\[ Q_d = 147 - 20P \]<br />\[ Q_d = 147 - 20(1.40) \]<br />\[ Q_d = 147 - 28 \]<br />\[ Q_d = 119 \]<br /><br />The shortage is the difference between the quantity demanded and the quantity supplied at this price:<br /><br />\[ \text{Shortage} = Q_d - Q_s \]<br />\[ \text{Shortage} = 119 - 110 \]<br />\[ \text{Shortage} = 9 \]<br /><br />Therefore, the exact shortage from the price ceiling is 9 gallons.