A small oil company has a refining budget of $20,000 and would like to determine the optimal product mix for profitability. The following table lists the costs and consumption of crude oil associated with its three products: Gasoline, Heating Oil, and Plastic Resin. For example, producing one gallon of Gasoline costs $0.40 in the refining process, incurs a storage cost of $0.10, and consumes 10 gallons of crude oil. Suppose the company has a budget of $5,000 for storage, and has 750,000 gallons of crude oil available. The profit margins of each gallon of gasoline, heating oil, and plastic resin are 14 cents, 10 cents, and 30 cents, respectively. By the nature of the refining process, the ratio between the gallons of heating oil produced and the gallons of gasoline produced is 2 . Assume that the demand for all three products is ample such that whatever is produced can be sold. (a) Please help the manager to formulate an optimization problem to decide the product mix that maximizes the total profit from selling the three products. [ 6pts] (b) Excel Solver is used to solve the above LP problem. Below is the manager's input into a spreadsheet, where relevant information is entered in columns A, B, C, D and rows 1 to 9. - In setting up the Solver, the manager needs to enter the target cell (objective function), the changing cells (decision variables), and the constraints. Which cell is the target cell (objective)? Which cells are the changing cells (variables)? [2 pts] - What is the formula (not the number) that the manager should enter in the cell B4? [2 pts] B4= - What is the formula (not the number) that the manager should enter in the cells B6, B7, and B8, respectively? [3 pts] B6=B7=B8= - What is the formula (not the number) that the manager should enter in the cells B9 and D9, respectively? [2 pts] B9=D9= (c) After solving the above LP in excel, the manager observes that the optimal production quantities given by the excel solver are as follows: Can you infer the shadow price of Crude Oil based on the above solutions? If you can, give the shadow price of crude oil below and explain your reasoning. If you cannot, explain why in one or two sentences. (3 pts)