John's Manufacturing makes four closely related products, which use some of the same inputs. The company has just received an order for 600 units of Product 1, 300 units of Product 2, 400 units of Product 3, and 200 units of Product 4. While these are the minimum quantities required, and the customer will go elsewhere if the company is unable to supply these amounts, the customer would be happy to purchase an additional amount of each product up to 10% over the stated minimum. In the relevant production period, there are limited quantities available of the key inputs required to make the products. A table in the Excel file shows the amount of each input required to make a unit of each product and the quantity of each input available. If they don't have enough capacity, the company can purchase some finished product from a third party to help meet their customer's request. A table in the Excel file shows the contracted prices their customer has agreed to pay for each product, the unit costs required to make each product, and the prices they pay to buy each product from the third party. The company's objective is to determine how many units of each product to make and, if necessary, how many units of each product to buy from the third party to maximize the profit earned from meeting their customer's minimum request, and potentially supplying additional units up to the maximum amounts their customer is willing to buy.

Product 1 Product 2 Product 3 Product 4 $650 $750 $500 $900 Price Paid by Customer Unit Cost to Make Price to Purchase from 3rd-Party Supplier $400 $600 $200 $800 $550 $750 $300 $1,000 Input 1 Input 2 Input 3 Input Requirements per Unit Product 1 Product 2 Product 3 5 15 5 25 18 0 0 15 20 00 UN Product 4 Input Availability 10 4,000 20 5,000 25 10,000