Find the ratios of products A, B, and C using a closed model. a. 8: 10: 40 b. 8: 13: 32 c. 8: 10: 3 d. 32: 40: 13 Anne and Nancy use a metal alloy that is 28% copper to make jewelry. How many ounces of a 24% alloy must be mixed with a 30% alloy to form 111 ounces of the desired alloy? a. 37 ounces b. 74 ounces c. 79 ounces d. 39 ounces There were 28,000 people at a ball game in Los Angeles. The day's receipts were $166,000. How many people paid $13 for reserved seats and how many paid $4 for general admission? a. 22,000 paid $13; 6000 paid $4. b. 6000 paid $13; 22,000 paid $4. c. 13,500 paid $13; 14,500 paid $4. d. 14,500 paid $13; 13,500 paid $4. Use the echelon method to solve the system of two equations in two unknowns. x + 2y = -7 -7x + 3y = 49 a. (-6, -7) b. (-7, 0) c. (7, -1) d. No solution Use the echelon method to solve the system. - = + = a. b. c. d. Find the inverse, if it exists, for the matrix. a. b. c. d. Wally's Warehouse sells trash compactors and microwaves. Wally has space for no more than 82 trash compactors and microwaves together. Trash compactors weigh 23 pounds and microwaves weigh 59 pounds. Wally is limited to a total of 8700 pounds for these items. The profit on a microwave is $99 and on a compactor $45. How many of each should Wally stock to maximize profit potential? a. 1 trash compactor, 81 microwaves b. 82 trash compactors, 1 microwave c. 0 trash compactors, 81 microwaves d. 0 trash compactors, 82 microwaves Provide an appropriate response. Is it possible that the feasible region of a linear program include more than one distinct area? a. No b. Yes Provide an appropriate response. It is possible to have a system of linear inequalities with a feasible region that includes more than one enclosed region. True or false? a. true b. false Provide an appropriate response. Does a linear program with at least three constraints always have a closed feasible region? a. Yes b. No Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function. z = 19x - 21y a. Maximum of -126; minimum of 0 b. Maximum of -81.25; minimum of -126 c. Maximum of 95; minimum of 0 d. Maximum of 95; minimum of -126 Provide an appropriate response. What is the smallest number of inequalities needed to produce a bounded feasibility region? a. 3 b. 1 c. 2 d. 4 Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function. z = 6x + 6y. a. Maximum of 42 minimum of 24 b. Maximum of 36 minimum of 30 c. Maximum of -24 minimum of -42 d. Maximum of 60; minimum of 24 Graph the linear inequality. x + y < -2 a. b. c. d. Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function. z = 21x + 5y + 12 a. No maximum; minimum of 17 b. No maximum; minimum of 12 c. No maximum; minimum of 33 d. No maximum; minimum of 38 A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim. It costs the company $1.63 to make each dog and $1.92 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the dual objective function? a. 1, 2, 1.63 b. 300, 700, 230 c. 1, 4, 1 d. 1.63, 1.92 Pivot once about the circled element in the simplex tableau, and read the solution from the result. a. x1 = 50, s2 = 200, z = 100; x2, x3, s1, s3 = 0 b. x1 = 50, s2 = 200, s3 = 300, z = 100; x2, x3, s1 = 0 c. x1 = 50, s3 = 300; x2, x3, s1, s2 = 0 d. x1 = 50, z = 100; x2, x3, s1, s2, s3 = 0 A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim. It costs the company $1.65 to make each dog and $1.52 for each dinosaur. What is the company's minimum cost? a. $228 b. $317 c. $289 d. $362 Pivot once about the circled element in the simplex tableau, and read the solution from the result. a. x1 = 48, s2 = -16, z = -48; x2, x3, s1 = 0 b. x1 = 24, s2 = -16, z = -24; x2, x3, s2 = 0 c. x1 = 48, s2 = 16, z = 48; x2, x3, s1 = 0 d. x1 = 24, s2 = -16, z = 24; x2, x3, s1 = 0 An electronics store stocks VCRs, stereo systems, and television sets. They have limited storage space and can stock a total of at most 180 of these three machines. They know from past experience that they should stock twice as many VCRs as stereo systems and at least 30 television sets. If each VCR sells for $500, each stereo system sells for $1900, and each television set sells for $600, how many of each should be stocked and sold for maximum revenues? a. 75 VCRs, 75 stereo systems, 30 television sets b. 90 VCRs, 45 stereo systems, 45 television sets c. 70 VCRs, 35 stereo systems, 75 television sets d. 100 VCRs, 50 stereo systems, 30 television sets A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim. It costs the company $1.33 to make each dog and $1.89 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the constraint inequality for trim? a. 1, 2 b. 1.33, 1.89 c. 4, 3 d. 1, 1 A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim. It costs the company $1.09 to make each dog and $1.31 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the dual objective function? a. 1.09, 1.31 b. 300, 700, 230 c. 1, 4, 1 d. 1, 2, 1.09 Find the transpose of the matrix. a. b. c. d. Pivot once about the circled element in the simplex tableau, and read the solution from the result. a. x3 = 14, s2 = 12, s3 = -4, z = 42; x1, x2, s1 = 0 b. x3 = 14, s2 = 12, s3 = 4, z = 42; x1, x2, s1 = 0 c. x3 = 14, s2 = -12, s3 = 4, z = -42; x1, x2, s1 = 0 d. x3 = 14, s2 = -6, s3 = 4, z = 42; x1, x2, s1 = 0 An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $540 and each Polar sells for $780. Up to 320 refrigerators can be stored in the warehouse and new refrigerators are delivered only once a month. It is known that customers will buy at least 60 Cool-Its and at least 120 Polars each month. How many of each brand should the store stock and sell each month to maximize revenues? a. 75 Cool-Its and 245 Polars b. 200 Cool-Its and 120 Polars c. 60 Cool-Its and 260 Polars d. 260 Cool-Its and 190 Polars Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated. $5400 at 6% compounded quarterly for 7 yr a. $8193.00 b. $3591.31 c. $3559.14 d. $1840.86 Find the payment necessary to amortize the loan. $8500; 12% compounded monthly; 48 monthly payments a. $223.84 b. $220.28 c. $224.00 d. $1024.44 Find the simple interest. Assume a 360-day year. Round results to the nearest cent. $26,000 at 2% for 109 days a. $520.00 b. $157.44 c. $156.00 d. $26,157.44 A small company borrows $29,000 at 11% compounded monthly. The loan is due in 2 years. How much interest will the company pay? a. $7100.03 b. $36,100.03 c. $6772.12 d. $7029.04 Find the compound amount for the deposit. Round to the nearest cent. $5000 at 10% compounded semiannually for 10 years a. $8144.47 b. $13,266.49 c. $12,968.71 d. $10,000.00 Find the compound amount for the deposit. Round to the nearest cent. $1370 at 11% compounded annually for 5 years a. $2123.50 b. $2308.53 c. $1972.80 d. $2079.76 Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated. $8000 at 8% compounded semiannually for 2 yr a. $9358.87 b. $1161.57 c. $6858.71 d. $6838.43 Find the simple interest. Assume a 360-day year. Round results to the nearest cent. $2680 at 1.60% for 114 days a. $13.46 b. $2680.00 c. $42.88 d. $13.58 Find the simple interest. Assume a 360-day year. Round results to the nearest cent. $12,920 at 10.80% for 67 days a. $259.69 b. $12,920.00 c. $255.82 d. $1395.36 How long will it take for prices in the economy to double at a 2% annual inflation rate? Round answer to the nearest year. a. 36 years b. 13 years c. 25 years d. 45 years