Maximizing Profit: Calculating Profit for a Company's Production

For a certain company, the cost for producing x items is 45x+300 and the revenue for selling x items is 85x−0.5x^2 a)Profit= Revenue - Cost P=(85x-0.5x^2) -(45x+300)* combined like terms (85x-40x=40x) P=85x-.5^2-45x-300 P=-.5x^2-40x-300 b)Given profit=300 -.5x^2-40x-300=300 subtract 300 from both sides to get -.5x^2-40x-600=0 Using the quadratic formula X=-b (+,-) sqrt(b^2-4ac)/2a Let a=-0.5 b=40 c=-600 So we have X=-40(+,-)sqrt(40^2-4(-.5)(-600)/2(-.5) *simplify numerator (40^2=1600) (-4*-.5=2) (2*-600=-1200) )(1600-1200=400) X=-40(+,-)sqrt(400)/2(-.5) *simplify the sqrt of 400 = 20 X=-40(+,-)20/2(.-5) *simplify the denominator 2(-.5)=-1 X=-40(+,-)20/-1 * solve the equation using +20 and -20 (-40-20=-60/-1 or 60) (-40+20=-20/-1 or 20 X=(60;20) c)Given profit=15000 15000=-.5x^2-40x-300 *subtract 15000 from both sides 0=-.5x^2-40x-15300 Using the quadratic formula X=-b (+,-) sqrt(b^2-4ac)/2a Let a=-.5 b=40 c=15300 So we have X=-40(+,-)sqrt(40^2-4(-.5)(-15300)/2(-.5) *simplify numerator (40^2=1600) (-4*-.5=2) (2*-15300=-30600) (1600-30600=-29000) X=-40(+,-)sqrt(-29000)/2(-.5) * You can't simplify the sqrt(-29000) so a profit of $15000 cannot be made