Section 4

Problem 1:
Develop the function within?, which consumes three numbers representing the x and y coordinates of a point and the radius r of a circle centered around the origin It returns `true` if the point is within or on the circle. It returns `false` otherwise. The distance of the point to the origin is the square root of x2 + y2.

Problem 2:
A local discount store has a policy of putting labels with dates on all of its new merchandise. If an item has not sold within two weeks the store discounts the item by 25% for the third week, 50% for the fourth week, and 75% for the fifth week. After that no additional discounts are given.

Develop the function new-price, which takes the initial price of an item and the number of weeks since the item was dated and produces the selling price of the item.

Problem 3:
A manufacturing company measured the productivity of its workers and found that between the hours of 6am and 10am they could produce 30 pieces/hour/worker; between 10am and 2pm they could produce 40 pieces/hour/worker; and between 2pm and 6pm they could produce 35 pieces/hour/worker.

Develop a function that takes an hour of the day between 6am and 6pm, in twenty-four hour format, along with the number of workers and computes the total number of pieces produced during that hour.

Problem 4:
An Internet service provider charges a base rate per megabyte (MB) transferred depending on market conditions. In addition to the base, transfers between 100 and 500 MB are charged an additional \$0.05/MB plus 33% of the base. Data transfers between 500 MB and 1500 MB are charged 1.44 times the base plus \$0.08/MB. Above 1500 MB the rate is simply twice the base. All data in a transfer is charged the same rate. For example, if 1600 MB are transfered, then the charge for all 1600 MB is twice the base.

Develop the function bill-amount, which takes an amount of data transferred in megabytes and a base rate in dollars and computes the total charge.

Problem 5:
Develop a function to calculate total tax liability for ANY given income. Assume that the share of income \$35,000 and below is federally taxed at 15%, the share of income between \$35,000 and \$100,000 is taxed at 25%, and the share of income over \$100,000 is taxed at 35%. Assume that there is no state income tax for income up to \$50,000 but is a flat 5% for all income above \$50,000.

 Jamie Raymond Matthias Felleisen 01 december 2003