Question

2. A new store is opening and needs to stock their shelves with product. They have a budget of X dollars to initially spend to stock the store. The store manager needs to decide which products to buy (and then sell) in the hopes of turning the greatest profit. The catalogue of items lists for each item, the available quantity, wholesale cost for purchase as well as MSRP (manufacturers suggested retail price The store manager decides to do his homework and creates a table listing for each item, m, the MSRP per unit, ci the cost per unit and available quantity qi in units. For example, the following might be the table for 4 items: Item 2 Cost/unit ci MSRP mi Available Quantity i 30 200 500 200 A BC D $40 $100 $20 $25 $100 $240 $80 $75 The Available Quantity refers to the quantity in stock available to purchase (Note that any fraction of this quantity may be purchased). The MSRP is the suggested retail price and the Cost is the wholesale cost. The profit made by a store is defined to be the MSRP - Cost. Suppose for this example, the total budget is X $16K, one can verify that if the store keeper buys all of products D and C and 5/6 the available quantity of A, (s)he will have spent $16K and total profit will be maximized at $41500. Help the store keeper by providing an algorithm to determine which items to select and in what quantity to maximize profit.