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.  

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98