Fitness Sneaker Company manufactures and sells sneakers. During each of the next six months, it forecasts the following demand (in pairs of sneakers): Month Demand 5 6 1 | 2 | 3 | 4 6000 5000 8000 4000 7000 5000 All demand must be met during that month. Each sneaker is made by workers and requires 20 minutes per pair. Each worker works 200 hours per month and can work up to 40 hours in overtime per month. Workers are paid a salary of $3000 per month, plus $75 per hour of overtime. Prior to each month's production, Fitness Sneakers can either hire additional workers or lay off some of its current workers. Due to administrative and other expenses, it costs $2000 to hire a worker and $3000 to fire a worker. Currently, at most 3000 pairs of sneakers can be stored in inventory, and his number is calculated at the end of the month (after all production). Each stored pair costs $5 per month in storage fees. Assume that there are 15 workers and 1000 pairs of sneakers in storage at the beginning of month 1. (a) Write down a linear programming model that minimizes the company's cost of meeting the demand. You do not need to write a data-independent model, a specific model for this particular instance with numbers is fine!