The demand equation for 6’ by 4’ outdoor garden shed isD(q) = – 4q^2 – 2q + 1,500where D(q) is the price in dollars at which q units are demanded. Find the quantity demanded in a day if the price of the shed is $1,480.

Accepted Solution

Answer:[tex]q=2[/tex]Step-by-step explanation:We need to find the quantity demanded if the price of the shed is 1480$. Hence:[tex]D(q)=1480=-4q^{2}-2q+1500[/tex]Sustract 1480 to both sides:[tex]-4q^{2} -2q+20=0[/tex]Multiply both sides by [tex]\frac{-1}{4}[/tex][tex]q^{2}+\frac{1}{2}q-5=0[/tex]We have a quadratic equation, we can solve it using the cuadratic formula or simply factoring it:[tex](q+\frac{5}{2})(q-2)[/tex]Now the solutions are given by:[tex]q_1=-\frac{5}{2} \\q_2=2[/tex]Since we look for a coherent answer we take the positive solution [tex]q_2[/tex]So the quantity demanded is [tex]q=2[/tex]