1. The Charm City ClothiersInc. makes coats and slacks. The two resources required are wool cloth andlabor. The company has 200 square yards of wool and 300 hours of labor available.Each coat requires 5 square yards of wool and 10 hours of labor, whereas eachpair of slacks requires 6 square yards of wool and 4 hours of labor. The profitfor a coat is $15, and the profit for a pair of slacks is $10. The companywants to determine the number of coats and pairs of slacks to make so that profitwill be maximized.

a. Formulate a linear programming model for this problem.

b. Solve this model by hand using the Corner Pointsgraphical method.

2. Solve the following linearprogramming model graphically. In addition, write the problem in standard formand do a constraint analysis for the optimal solution.

Maximize14x + 20y

Subjectto

x + 2y <20

x + y <15

x >8

x, y 0

3. Copperfield Mining Companyowns two mines, each of which produces three grades of ore high, medium, andlow. The company has a contract to supply a smelting company with at least 150tons of high-grade ore, 120 tons of medium-grade ore, and 150 tons of low-gradeore. Each mine produces a certain amount of each type of ore during each hourthat it operates. Mine 1 produces 6.5 tons of high-grade ore, 3.2 tons ofmedium-grade ore, and 4.8 tons of low grade ore per hour. Mine 2 produces 3.2,4.0, and 9.8 tons, respectively, of high-, medium-, and low-grade ore per hour.It costs Copperfield $400 per hour to operate mine 1, and it costs $280 per hourto operate mine 2. The company wants to determine the number of hours it needsto operate each mine so that its contractual obligations can be met at thelowest cost.

Formulate a linear programming model for this problem.

Note: Do NOT solve the model after formulating.

4. Determine whether thefollowing linear programming problem is infeasible, unbounded, or has multipleoptimal solutions. Draw a graph and explain your conclusion.

Maximize80x + 60y

Subjectto

-3x + 4y< 60

2x + 3y> 60

2x + y >40

x, y 0

Some of the questions aboverequire drawing graphs. Here is a list of options for you to include a graph inyour answer.

Draw the graph using MS Paintor CorelDraw or some other software. Copy the graph in a MS Word file and postthe file on the course website in appropriate category.

OR

Draw the graph by hand on apaper, scan it and post it with your answer.

OR

Describe the graph in wordsin your answer.