SECTION 11.7 Systems of Inequalities 839 55. x y 40 20 (20, 30) (20, 20) (0, 15) (0, 50) (15, 15) 50 30 10 56. x y 10 5 22 (5, 6) (5, 2) (4, 0) (0, 3) (0, 6) 7 24 Applications and Extensions 57. Financial Planning Juliana entered a raffle contest through a local radio station and won $5000. She decides to invest the money to help buy a new car when she graduates from college in two years. As a financial adviser, you recommend that Juliana invest at least $3500 in Treasury bills yielding 1% and at most $1000 in corporate bonds yielding 3%. (a) Using x to denote the amount of money invested in Treasury bills and y to denote the amount invested in corporate bonds, write a system of linear inequalities that describes the possible amounts of each investment. (b) Graph the system and label the corner points. 58. Manufacturing Trucks Mike’s Toy Truck Company manufactures two models of toy trucks, a standard model and a deluxe model. Each standard model requires 2 hours (h) for painting and 3 h for detail work; each deluxe model requires 3 h for painting and 4 h for detail work.Two painters and three detail workers are employed by the company, and each works 40 h per week. (a) Using x to denote the number of standard-model trucks and y to denote the number of deluxe-model trucks, write a system of linear inequalities that describes the possible numbers of each model of truck that can be manufactured in a week. (b) Graph the system and label the corner points. 59. Blending Coffee Bill’s Coffee House, a store that specializes in coffee, has available 75 pounds (lb) of A grade coffee and 120 lb of B grade coffee. These will be blended into 1-lb packages as follows: an economy blend that contains 4 ounces (oz) of A grade coffee and 12 oz of B grade coffee, and a superior blend that contains 8 oz of A grade coffee and 8 oz of B grade coffee. (a) Using x to denote the number of packages of the economy blend and y to denote the number of packages of the superior blend, write a system of linear inequalities that describes the possible numbers of packages of each kind of blend. (b) Graph the system and label the corner points. 60. Mixed Nuts Nola’s Nuts, a store that specializes in selling nuts, has available 90 pounds (lb) of cashews and 120 lb of peanuts. These are to be mixed in 12-ounce (oz) packages as follows: a lower-priced package containing 8 oz of peanuts and 4 oz of cashews, and a quality package containing 6 oz of peanuts and 6 oz of cashews. (a) Use x to denote the number of lower-priced packages, and use y to denote the number of quality packages. Write a system of linear inequalities that describes the possible numbers of each kind of package. (b) Graph the system and label the corner points. 61. Transporting Goods A small truck can carry no more than 1600 pounds (lb) of cargo and no more than 150 cubic feet ft3 ( ) of cargo. A printer weighs 20 lb and occupies 3 ft3 of space. A microwave oven weighs 30 lb and occupies 2 ft3 of space. (a) Using x to represent the number of microwave ovens and y to represent the number of printers, write a system of linear inequalities that describes the number of ovens and printers that can be hauled by the truck. (b) Graph the system and label the corner points. 62. Challenge Problem Graph the system of inequalities. x y y x 4 3 2 + ≤ ≤ − ⎧ ⎨ ⎪⎪ ⎩ ⎪⎪ Retain Your Knowledge Problems 63–72 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 63. Solve x 2 1 8 0 2 ( ) + + = in the complex number system. 64. Write the polar equation r3 sinθ = as an equation in rectangular coordinates. Identify the equation and graph it.
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