Hello i have to do this case with Excel and put the equations in Lingo (Lindo)

A company markets a product in three different presentations, small, medium and large. The utility of the large size is $ 55, that of the small size is $ 38 and that of the medium size $ 49 per unit. Since it is a very successful product, demands for 6505, 6685 and 6095 units of the small product are committed for the next three months. Also 5010, 5185 and 5405 units of the medium product and 4495, 4205 and 4745 units of the large product. After analyzing the production process it has been found that a machine is the bottleneck. The time availability of this machine every month is 240 hours. The manufacturing time in the bottleneck machine for the small product is 1.0 minute, that of the medium product is 1.1 minutes and that of the large product is 1.3 minutes per unit. In order to handle demand fluctuations, the company can store up to 400 products per month regardless of product size, although the monthly storage cost is $ 4, $ 6 and $ 8 per unit for small, medium and large products respectively. Initially there are 70 large, 30 medium and 100 small products. By management strategy at the end of the third month there must be 80 large, 40 medium and 70 small products. You can also request that the machine work overtime. However, the utility of the products drops to $ 54, $ 47 and $ 38 for large, medium and small products respectively. The extra time available for each month is 110 hours, 90 hours and 100 hours.

For each of the following questions consider that they are independent of each other and are based on the result you get for question a) You are asked as production manager to determine how many pieces of each type to make per month in normal time and overtime to maximize profits at the end of the three months. What would be your solution if the inventory space is now expanded to 500 pieces per month? Would you change your solution if you now only have 100 hours of overtime available in the first month? How much would you be willing to pay for an additional minute of extra time in each month? What would be the new solution if now the inventory costs are 12, 10 and 8 respectively for large, medium and small products. What would be your solution if for maintenance purposes the bottleneck machine is not available for 10 hours of normal time during the first month? A maintenance consulting company offers you a plan for the bottleneck machine in which you increase 60 hours per month of availability for the machine. If the cost of this plan is 90,000 per month, should you accept your proposal? What would be your response if inventory costs are now zero? Would it be feasible to meet the demand for the products if during the first month they are now 7000, 4800 and 4000 for small, medium and large sizes? What would be your solution if you now have 300 hours per month of production in normal time? What would be your solution if you now only have 220 hours of normal time in each month? Would it be feasible to achieve production?