The supply equation for an olive oil press isS(q) = 5q^2 + 1,000q + 100where S(q) is the price in dollars at which q units are supplied. Find the quantity supplied in a month when the company sets the price of its olive oil press at $12,820

Answer:12 unitsStep-by-step explanation:The given function is[tex]S(q) = 5q^2 + 1000q + 100[/tex]where, S(q) is the price in dollars at which q units are supplied.We need to find the quantity supplied in a month when the company sets the price of its olive oil press at $12,820.Substitute S(q)=12820 in the given function.[tex]12820 = 5q^2 + 1000q + 100[/tex]Subtract both sides by 12820.[tex]0= 5q^2 + 1000q - 12720[/tex]Taking out GCF.[tex]0= 5(q^2 + 200q - 2544)[/tex]Now solve the equation for q by splitting the middle term.[tex]0= 5(q^2 + 212q-12q - 2544)[/tex][tex]0= 5(q(q + 212)-12(q + 212))[/tex][tex]0= 5(q + 212)(q-12)[/tex]Using zero product property we get[tex]q + 212=0\Rightarrow q=-212[/tex][tex]q-12=0\Rightarrow q=12[/tex]q is number of units. So the value of q can not be negative.Therefore the quantity supplied in a month when the company sets the price of its olive oil press at $12,820 is 12 units.