The fixed ordering costs are £ “0.3*x” for 10 grams of gold, and the holding cost for the same quantity is £0.4 per year. Assume the manufacture's weekly requirement is in average “x * 10kg” but may go up to “(x + 2) * 10kg”. The current average gold price is £26/gram. The lead time for ordering is usually 5 days.

a. Evaluate how much gold you should purchase at once.

b. Decide how often you need to order.

c. Calculate the safety stock and explain its usefulness.