The following data is for a crowbar purchased for resale by a regional hardware distributor. Monthly crowbar demand is 10,000 units and is constant over the year. The cost of placing an order is $100 per order. The unit cost of the item from the manufacturer is $30 per crowbar. Assume an annual carrying cost rate of i = 0.2. Double check your units all match (demand and i). 1. Calculate the economic order quantity, Q∗ and the minimum cost of operating the system (K(Q∗)) when ordering the optimal lot size. 2. Assuming you order Q∗ units each time, how many orders will you place per year? 3. What is the long-term average inventory level? 4. Calculate the percentage increase in cost if you increase Q∗ by 20% (Note whether you include procurement cost in your calcu- lations. Up to you as to whether to do that or not, just be sure to label.) When does Q equal Q*? Difficulty: [★ ★ ★ ☆ ☆] For the simple EOQ model, show that the average annual inven- tory carrying charges are equal to the average annual ordering costs when Q = Q*. A recommendation for thinking about this question is to calculate the inventory costs, order costs, procurement costs, and total costs separately and see how they vary for different values of Q. A complete answer to this question will contain a mathematical description of why this is true