Question 1180677
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Profit = Revenue minus Cost<br>
Revenue is 110x-0.5x^2; cost is 70x+300; you want the profit to be 300:<br>
{{{300=(110x-0.5x^2)-(70x+300)}}}
Simplify and combine like terms on the right
{{{300=-0.5x^2+40x-300}}}
Get everything on one side of the equation with a positive coefficient on the x^2 term
{{{0.5x^2-40x+600=0}}}
Multiply by 2 to clear fractions to make the quadratic easier to factor
{{{x^2-80x+1200=0}}}
Factor the quadratic; this one factors nicely
{{{(x-20)(x-60)=0}}}<br>
ANSWER: A profit of $300 can be obtained by producing and selling EITHER 20 units or 60 units.<br>