A person decides to start trying to make a profit from their knitting hobby. They knit caps and sweaters. Sweaters require 850 yards of wool, 50 hours of labor, and 4 units of dye. Caps require 95 yards of wool, 12 hours of labor, and 2 units of dye. The person has access to 12000 yards of wool and 140 units of dye. They're willing to work for 1000 hours total producing sweaters and caps. Caps sell for a profit of $80 and sweaters for a profit of $400.

a. Create a spreadsheet that would determine how much wool, labor, and dye it would take, and how much profit they would make by producing a given number of sweaters and caps.
b. Use solver to determine the number of caps and sweaters they should make that would maximize their profit. Assume for the time being that they can produce fractional sweaters and caps.
c. The knitter is considering changing the amount they'd charge per cap. How much could their profit per cap increase or decrease by before their optimal strategy would change?
d. The knitter is considering working more hours. How much more would they make per additional hour of labor? How many hours could they add to their schedule before this answer changed?