MAT 114 Quiz 4 Fall 2015 Name ______________________________________________________ Section ____________ Answer each of the following carefully and completely. Be sure to show all work for the sake of partial credit. 1. Sketch the region that corresponds to the given set of inequalities. Determine whether the region is bounded or unbounded, and find the coordinates of all corner points (if any). 3 x+2 y 6 3 x2 y 6 y 2 2. Gerber Mixed Cereal for Baby contains, in each serving, 60 calories, 11 grams of carbohydrates, and no vitamin C. Gerber Apple Banana Juice contains, in each serving, 60 calories, 15 grams of carbohydrates, and 120 percent of the U.S. Recommended Daily Allowance (RDA) of vitamin C for infants. You want to provide your child with at least 120 calories, at least 26 grams of carbohydrates, and at least 50 percent of the U.S. RDA of vitamin C for infants. Draw the feasible region that shows the number of servings of cereal and the number of servings of juice that you can give your child. Find the corner points of the region. 3. Minimize the cost function C=x+ 2 y given the following constraints: x+3 y 30 2 x + y 30 x0 y0 4. Maximize the profit function P=x + y given the following constraints: x+ 2 y 10 4 x + 4 y 20 6 x+ 3 y 30 x0 y0 5. You manage an ice cream factory that makes three flavors: Creamy Vanilla, Continental Mocha, and Succulent Strawberry. Into each batch of Creamy Vanilla go 2 eggs, 1 cup of milk, and 2 cups of cream. Into each batch of Continental Mocha go 1 egg, 1 cup of milk, and 2 cups of cream. Into each batch of Succulent Strawberry go 1 egg, 2 cups of milk, and 2 cups of cream. You have in stock 200 eggs, 120 cups of milk, and 200 cups of cream. You make a profit of $3 on each batch of Creamy Vanilla, $2 on each batch of Continental Mocha, and $4 on each batch of Succulent Strawberry. If you cannot make more than 10 batches of Succulent Strawberry due to a poor strawberry harvest, how many batches of each should you make to maximize your profit? 6. Minimize the cost function C=2 x +2 y +3 z given the following constraints: x+z 100 2 x + y 50 y + z 50 with x, y ,z non-negative