Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Maximize p = X + 2y subject to x+5y512 3X+y8 x20,y20. (X. y) Maximize p = 2x + y subject to x + 2y = 11 -X+ys5 x+ys5 X 20, y20. P = ( x, y ) =Maximize p = x subject to X - yE 8 -x + 3y 8 x 20, y 20. HINT [See Examples 1 and 2.] P = (x, y ) =You are in charge of purchases at the student-run used-book supply program at your college, and you must decide how many introductory calculus, history, and marketing text: should be purchased from students for resale. Due to budget limimtions, you cannot purchase more than 900 of these textbooks each semester. There are also shelfispace limitations: Calculus texE occupy 2 units of shelf space each, history books 1 unit each, and marketing texts 5 units each, and you can spare at most 1,500 units of shelf space for the texts. If the used book program makes a profit of $10 on each calculus text, $4 on each history text, and $8 on each marketing text, how many of each type of text should you purchase to maximize profit? HINT [See Example 3.] calculus text(5) E histowtexus) S marketing text(s) E What is the maximum profit the program can make in a semester? $: Solve the LP problem. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the region is empty. Enter UNBOUNDED if the function is unbounded.) Minimize c : X + 2y subject to x+5y228 3x+y228 x2 0, y20. c: M _( ) You manage an ice cream factory that makes two avors: 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 550 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 avor 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 E quarts