Sketch the region corresponding to the given inequalities. 3x + 2y 2 6 2x - 3y = 6 3x - 2y 2 0 x 20, y 20 y y 10 10 10 10 Solution Set S 5 Solution Solution Solution Set Set Set X X 10 -5 10 10 -5 5 10 10 -5 5 10 10 -5 5 10 -5/ -5 -5 10 10 Say whether the region is bounded or unbounded. O The region is bounded. O The region is unbounded. Find the coordinates of all corner points (if any). (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) (x, y) = (x, y) = (x, y) =Solve the given linear programming problem graphically. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x + 2y subject to 3x + y = 30 xty = 12 x + 3y = 30 x 2 0, y = 0. D= (x, v) =\fSolve the given linear programming problem using the simplex method. If no optimal solution exists. indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Maximize p : x + y + 22 subject to x+Zy+22 an 7x+y+32 ED x20.y20,220. mi ) S S You are the buyer for OHaganBooks. com and are considering increasing stocks of romance and horror novels at the new OHaganBooks.com warehouse in Texas. You have offers from several publishers: Duffin House, Higgins Press, McPhearson Imprints, and O'Conell Books. Duffin offers a package of 5 horror novels and 5 romance novels for $50, Higgins offers a package of 5 horror and 10 romance novels for $80, McPhearson offers a package of 10 horror novels and 5 romance novels for $80, and O'Conell offers a package of 10 horror novels and 10 romance novels for $90 How many packages should you purchase from Duffin House and Higgins Press to obtain at least 4,000 horror novels and 6,000 romance novels at minimum cost? Duffin House packages Higgins Press packages What is the minimum cost? $You manage an ice cream factory that makes two flavors: Creamy Vanilla and Continental Mocha. Into each quart of Creamy Vanilla go 2 eggs and 3 cups of cream. Into each quart of Continental Mocha go 1 egg and 3 cups of cream. You have in stock 500 eggs and 900 cups of cream. You make a profit of $3 on each quart of Creamy Vanilla and $2 on each quart of Continental Mocha. How many quarts of each flavor should you make to earn the largest profit? HINT [See Example 2.] (If an answer does not exist, enter DNE.) Creamy Vanilla quarts Continental Mocha quartsGerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates. Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates. If the cereal costs 30c per serving and the dessert costs 52c per serving, and you want to provide your child with at least 140 calories and at least 32 grams of carbohydrates, how can you do so at the least cost? (Fractions of servings are permitted. If an answer does not exist, enter DNE.) Gerber Mixed Cereal for Baby serving(s) Gerber Mango Tropical Fruit Dessert serving(s)Nutrition Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 246 grams of protein and at least 156 grams of fat. If chicken costs 94 per ounce and grain costs ic per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost? (If an answer does not exist, enter DNE.) grain OZ chicken ozSolve the given LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. HINT [See Example 1.] (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = x - 7y subject to 2x + y =4 x 20, y 20 (x, y ) = (Maximize p = x subject to X - 5 6 -x + 3y= 6 x 2 0, y20. HINT [See Examples 1 and 2.] P= (x, y) =