6 Jean knits items for charity. Each month the charity provides her with 75 balls of wool.
She knits hats and scarves. Hats require 1.5 balls of wool each and scarves require 3 balls each. Jean has 100 hours available each month for knitting. Hats require 4 hours each to make, and scarves require 2.5 hours each. The charity sells the hats for \(\pounds 7\) each and the scarves for \(\pounds 10\) each, and wants to gain as much income as possible. Jean prefers to knit hats but the charity wants no more than 20 per month. She refuses to knit more than 20 scarves each month.

1. Define appropriate variables, construct inequality constraints, and draw a graph representing the feasible region for this decision problem.
2. Give the objective function and find the integer solution which will give Jean's maximum monthly income.
3. If the charity drops the price of hats in a sale to \(\pounds 4\) each, what would be an optimal number of hats and scarves for Jean to knit? Assuming that all hats and scarves are sold, by how much would the monthly income drop?