Chapter 4 Quadratic Functions and Factoring - 4.7 Complete the Square - 4.7 Exercises - Problem Solving - Page 290: 65

Increasing the price by $100$

$y=(200+10x)(40-x)=-10x^2+200x+8000=-10(x^2-20x)+8000=-10((x-10)^2-100)+8000=-10(x-10)^2+1000+8000=-10(x-10)^2+9000$ Thus the vertex of the graph is at $(10,9000)$, and the shop can maximize its revenue by increasing the price by $ \$100$.