Question

A company can manufacture x hundred for a totally cost of C =200 + 1500x -100x^2 find x if the total cost is 5,800

Answer 1

`\begin{gathered} C=200+1500x-100x^2 \\ \text{Reordering} \\ C=-100x^2+1500x+200 \\ C=5800 \\ -100x^2+1500x+200=5800 \\ -100x^2+1500x+200-5800=0 \\ -100x^2+1500x+200-5600=0 \\ x=(-b\pm√(b^2-4ac))/(2a) \\ a=-100 \\ b=1500 \\ c=-5600 \\ x=\frac{-1500\pm\sqrt[]{(1500)^2-4(-100)(-5600)}}{2(-100)} \\ x=\frac{-1500\pm\sqrt[]{2250000-2240000}}{-200} \\ x=\frac{-1500\pm\sqrt[]{10000}}{-200} \\ x=(-1500\pm100)/(-200) \\ x1=(-1500+100)/(-200) \\ x1=(-1400)/(-200) \\ x1=7 \\ x2=(-1500-100)/(-200) \\ x2=(-1600)/(-200) \\ x2=8 \\ \text{The values }x\text{ hundred for the cost }is\text{ \$5,800 are 7 and 8} \end{gathered}`