ALL parts please !!!!!!
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 and 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 a third as much wool as cotton, and your distributor requires a minimum of 2,400 lbs total of cotton and wool when those materials are ordered. Finally, the factory requires at least 1,000 lbs of cotton for production. You hope to determine the total pounds of cotton and wool fibers for the company's next order from the distributor that minimizes cost. (a) [5 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. (b) [10 points] Solve the linear programming problem in part (a). Explain which method you used to solve the problem and why, and give a recommendation to the company regarding their monthly purchases of raw materials. This recommendation should include the minimum monthly cost incurred. (c) [5 points] Sensitivity Analysis: Suppose that the price of cotton varies between $0.50 and $2.00 per pound (rather than staying fixed at $1.80 per pound). Perform a sensitivity analysis on price of cotton, and explain how this price fluctuation affects the total cotton, wool, and minimum cost associated with the company's next order of raw materials. 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 and 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 a third as much wool as cotton, and your distributor requires a minimum of 2,400 lbs total of cotton and wool when those materials are ordered. Finally, the factory requires at least 1,000 lbs of cotton for production. You hope to determine the total pounds of cotton and wool fibers for the company's next order from the distributor that minimizes cost. (a) [5 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. (b) [10 points] Solve the linear programming problem in part (a). Explain which method you used to solve the problem and why, and give a recommendation to the company regarding their monthly purchases of raw materials. This recommendation should include the minimum monthly cost incurred. (c) [5 points] Sensitivity Analysis: Suppose that the price of cotton varies between $0.50 and $2.00 per pound (rather than staying fixed at $1.80 per pound). Perform a sensitivity analysis on price of cotton, and explain how this price fluctuation affects the total cotton, wool, and minimum cost associated with the company's next order of raw materials
