You run a small furniture business. You sign a deal with a customer to deliver up to 600 chairs, the exact number to be determined by the customer later. The price will be $130 per chair up to 500 chairs, and above 500, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over-ordered.
What is the largest revenue your company can make under this deal? What is the smallest revenue your company can make under this deal?

64,925‬

Minimum occurs at x = 0 when no chairs are sold. The price is $0.  

Step-by-step explanation:

solution

Let x be the number of chair greater than 500. Then price is  

P = (130-0.25*x)(500 +x)

For critical point,  

P'(x) = -0.5x + 15 = 0  

From here, we get x = 30. Using second derivative test, P"(x) = -0.5 for all x so global maximum occurs as the function is concave downward. The price is  

P(30) = (130 - 0.25*30)(500 + 30) = $64,925‬

Minimum occurs at x = 0 when no chairs are sold. The price is $0.  

parallel and congruent

step-by-step explanation:

the movement of translation is linear.   these have the same translation because you are using the same rule for each point of the triangle so you will see the same slope being used to get from a point on the triangle to its image.

same slope!   you should think parallel when you see those 2 word together (well unless it's the same line but it can't be because we are coming from different points here)

congruent! because each point is being moved the same distance.

step-by-step explanation: