S14.1. Barrows Textile Mills produces two types of cotton cloth-denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6500 pounds of cotton and 3000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. a. Formulate and solve a linear programming model for this problem. b. Solve this model using the graphical method. S14.2. The Tycron Company produces three electrical productsclocks, radios, and toasters. These products have the following resource requirements: The manufacturer has a daily production budget of $2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Clocks sell for $15, radios for $20, and toasters for $12. The company desires to know the optimal product mix that will maximize profit. Formulate and solve a linear programming model for this problem. in profit, each table, $275, and each chair, $190. The company wants to know how many pieces of each type of furniture to make per week in order to maximize profit. Formulate and solve a linear programming model for this problem. S14.4. The Pinewood Cabinet and Furniture Company produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture-wood, upholstery, and labor. The resource requirements for each piece of furniture and the total resources available weekly are as follows: The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of 500 pieces of furniture; however, a sofa takes up twice as much space as a table or chair. Each sofa earns $320 S14.16. The Copperfield Mining Company owns two mines that produce three grades of ore: high, medium, and low. The company has a contract to supply a smelting company with 12 tons of highgrade ore, 8 tons of medium-grade ore, and 24 tons of low-grade ore. Each mine produces a certain amount of each type of ore each hour it is in operation. The company has developed the following linear programming model to determine the number of hours to operate each mine (x1 and x2) so that contracted obligations can be met at the lowest cost: MinimizeZ=200x1+160x2(cost,$) subject to 6x1+2x22x1+2x24x1+12x2x1,x2128240(high-gradeore,tons)(medium-gradeore,tons)(low-gradeore,tons) a. Solve this model graphically. b. Solve the model using Excel