cKathryn Bollinger, September 26, 2011 1Week-In-Review #4 (3.1, 3.2, 3.3)1. Graph to find the solution set for each of the following systems of inequalities.Find all corner points and state whether the solution set is bounded or unbounded.(a) x − y ≤ 102x + 5y ≥ 20x > 4y ≥ 1(b) −0.5x + 4y ≤ 5y ≤ −2x−6 ≤ x ≤ 4y ≥ −82. Solve the following linear pr ogramming (LP) problem:(a) OBJECTIVE: Maximize R = 15x + 9ySUBJECT TO:x + y ≤ 5−x + 2y ≤ 63x − 4y ≤ 12x ≥ 0, y ≥ 0(b) Is there a minimum value of R subject to these constraints?3. Solve the following linear pr ogramming (LP) problem:(a) OBJECTIVE: Minim ize C = 10x + 15ySUBJECT TO:2x + 3y ≥ 12x − 3y ≤ 2x − y ≥ −3x ≥ 2y ≥ 2(b) Is there a maximum value of C subject to these constraints?cKathryn Bollinger, September 26, 2011 24. SET UP the following LP problem. DO NOT SOLVE.A baker has 600 pounds of chocolate, 100 pounds of nuts, and 50 pounds of fruit, w ith which tomake three types of candy, A, B, and C. A box of candy A uses 3 pounds of chocolate, 1 pound ofnuts, 1 pound of fruit, and it sells for $8. A box of candy B requires 4 pounds of chocolate, 1/2pound of nuts, and sells for $5. A box of candy C requires 5 pounds of chocolate, 3/4 pound ofnuts, 1 pound of fruit, and sells for $6. How many boxes of each type of candy should be madefrom the inventory available in order to maximize revenue?5. SET UP the following LP problem. DO NOT SOLVE.A rental company has two types of truck s; type A has 20 cu.ft. of refrigerated space and 40 cu.ft. ofnon-refrigerated space, and type B has 30 cu.ft. each of refrigerated and non-refrigerated space. Afood plant must ship at least 900 cu.ft. of refrigerated p roduce and 1200 cu .f t. of non-r efrigeratedproduce. If truck A r ents for 30 cents per mile and truck B rents for 40 cents per mile, then howmany of each truck should the plant rent in order to minimize rental costs?6. A company has 100 kg of dry cereal and 125 kg of chocolate candy to be used in making twodifferent snack mixes. One m ix will contain half cereal and half candy, and will sell for $6 p erkilogram. The other mix will contain 1/3 cereal and 2/3 candy, and will sell for $4.80 per kilogram.How m any kilograms of each mix should the company p repare for maximum revenue? What is themaximum revenue?7. A seamstress has 80 units of cotton material and 120 units of wool material. A suit requires1 unit of cotton and 3 un its of wool; a dress requires 2 units of each material. Due to previousdemand, it has been determined that at most 10 suits s hould be made. If each suit brings in $20profit and each dress brings in $30 of profit, how many of each garment should be produced inorder to maximize profit? Will there be any leftover resour ces when maximizing
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