Formulate and solve the following LPs in Excel. Use a single Excel file for all the problems -each problem should be done per tab. Use text boxes to directly answer the questions in the problem i.e., do not simply formulate \& solve the LP. Be sure that the tabs are labeled and arrange them in the same order as problems below. 1. (10 points) A beverage can manufacturer makes three sizes of soft drink cans- Small, Medium and Large. Production is limited by machine availability, with a combined maximum of 90 production hours per day, and the daily supply of metal, no more than 120 kg per day. The following table provides the details of the input needed to manufacture one batch of inn a...n cownah sima Develop a linear programming model to maximize profit and determine how many batches of each can size should be produced. For this particular problem explicitly do/write the following before solving the problem in Excel. - State the objective function in words. - State the constraints in words. - Define the decision variables. - Write/express the algebraic formulation of the LP. Answer the following questions: a. How many batches of each can size is produced at optimality? b. How many metal (kg) /batch will be used? Is there slack? c. If one more hour of machines' time is available/batch, what is the change in profit/batch? What is the new profit/batch? d. Provide a short report (one paragraph, 2-3 sentences) to discuss your results and how it can be used by the manager of the firm