4. A different textile manufacturer hires you to ensure that the workers on the factory floor have sufficient raw materials each month to meet output demands on their company. The manufacturer plans to place an order for cotton, wool, and polyester fibers from a distributor, and they seek your recommendation on how much of each raw material the company should order monthly. The cost of each fiber per pound is given in the following table: The linens produced by the factory require at least half as much wool as both cotton and polyester combined, and your distributor imposes a weight limit of 5,400 lbs of materials per order. Furthermore, the distributor requires a minimum of 2,400 lbs total of wool and polyester when those materials are ordered. Finally, the factory requires at least 1,500 lbs of cotton for production. You hope to determine the total pounds of cotton, wool, and polyester fibers for the company's next order from the distributor that minimizes cost. (a) [10 points] Define variables for this scenario, write down the objective function, and identify the constraints in this problem. In other words, write down the full linear programming problem that models this scenario. Solve the linear programming problem using simplex method. Show all steps