A gardener requires fertilizer to have a minimum of 80 units of nitrogen, 15 units of potassium and 10 units of iron. Two fertilizer mixes are available. Brand X contains 20, 2 and 1 units of the minerals, while Brand Y contains 4, 1, 2 units of the minerals respectively. Brand X costs $18 per kg while Brand Y costs 6 per kg.
(a) Write down the inequality constraints and the equation of the cost function.
(b) Graph the inequality constraints, Hence determine the number of Kg of each brand which provide the minimum mineral requirements at minimum cost.
(c) Confirm your answer in (b) algebraically.