In Problem (a) find the vertex of the graph of the equation, (b) determine if the vertex is a maximum or minimum point, (c) determine what value of x gives the optimal value of the function, and (d) determine the optimal (maximum or minimum) value of the function.

Micah's gym is moving into a bigger space, where he can have more stationary bicycles and treadmills in his gym. Let x be the number of treadmills and y be the number of bicycles. The number of new bicycles must be more than 1/3 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650. Select ALL the constraints for this situation. 1.) 670x + 340y 0 3.) x > 0 4.) x > 1/3y 5.) 670x + 340y < 5650 6.) y > 1/3x

A car rental agency rents 300 cars per day at a rate of $55 per day. For each $1 increase in the per-day rate, 3 fewer cars are rented. They want to know what price they should rent at to maximize their revenue. Help them get started by setting up the revenue equation. You do not need to find the optimal price, just set up the revenue equation. Use x as your variable, but in your work be sure to define what a represents. Revenue =

Draw the graph of y = 3x2 + 6x − 24 and label its minimum.