Explain Linear programming model for bicycle manufacturer

A bicycle manufacturer is determining its production schedule for the next 6 months. Assume that it costs this company $150 to manufacture each bicycle. At the end of each month, a holding cost of $35 per bicycle left in inventory is incurred. No more than 40 bicycles can be stored in inventory at any point in time. Monthly demands for bicycles are projected to be as follows: 150 in month 1; 175 in month 2; 165 in month 3; 156 in month 4; 169 in month 5; and 178 in month 6. Assume that at the beginning of month 1, 10 completed bicycles are in inventory. Finally, this company can produce up to 170 bicycles per month. Formulate and solve a linear programming model to find a cost-minimizing production schedule that meets all demands on time.

Answer the following questions-

1) Write down the decision variables.

2) Write down the optimization statement for the objective function.

3) Write down the constaints.

4) With Excel Solver, what is the optimal production schedule? (Please hand in a printed copy of the report)

5) By Excel Solver, what is the sensitivity report? (Please hand in a printed copy of the report)