8. A chemical company produces two products \(X\) and \(Y\). Based on potential demand, the total production each week must be at least 380 gallons. A major customer's weekly order for 125 gallons of \(Y\) must be satisfied. Product \(X\) requires 2 hours of processing time for each gallon and product \(Y\) requires 4 hours of processing time for each gallon. There are 1200 hours of processing time available each week. Let \(x\) be the number of gallons of \(X\) produced and \(y\) be the number of gallons of \(Y\) produced each week.

1. Write down the inequalities that \(x\) and \(y\) must satisfy.
   (3) It costs \(\pounds 3\) to produce 1 gallon of \(X\) and \(\pounds 2\) to produce 1 gallon of \(Y\). Given that the total cost of production is \(\pounds C\),
2. express \(C\) in terms of \(x\) and \(y\).
   (1) The company wishes to minimise the total cost.
3. Using the graphical method, solve the resulting Linear Programming problem. Find the optimal values of \(x\) and \(y\) and the resulting total cost.
4. Find the maximum cost of production for all possible choices of \(x\) and \(y\) which satisfy the inequalities you wrote down in part (a).