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2.2 Problems3. Write the augmented matrix2x+y+z=33x-4y+2y=-7x+y+z=27. Write the system of equations1000100014-5113. Replace R1 by (-2)R2+R116403205375715. Replace R1 by (1/3)R1300050004189817. Use Gauss Jordan method, or upper triangular method to solve each systemx+y=53x+2y=1219.x+y=74x+3y=2221.2x-3y=24x-6y=123.6x-3y=1-12x+6y=-225.y=x-3y=1+zz=4-x27.2x-2y=-52y+z=02x+z=-729.4x+4y-4z=242x-y+z=-9x-2y+3z=144. The president of Sam’s Supermarkets plans to hire two public relations firms to survey 500 customers by phone, 750 by mail, and 250 by in person interviews. The Garcia firm has personnel to do 10 phone surveys, 30 mail surveys, and 5 interviews per hour. The Wong firm can handle 20 phone surveys, 10 mail surveys, and 10 interviews per hour. For how many hours should each firm be hired to produce the exact number of surveys needed.49. The U-Drive Rent-A-Truck company plans to spend 7 million on 200 new vehicles. Each commercial van will cost $35,000, each small truck $30,000, and each large truck $50,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy?50. To get the necessary funds for a planned expansion, a small company took out three loans totaling $25,000. Company owners were able to get interest rates of 8%, 9%, and 10%. They borrowed $1000 more at 9% than they borrowed at 10%. The total amount of interest on the loans was $2190.a. How much did they borrow at each rate?b. Suppose we drop the condition that they borrowed 1000 more at 9% than they did at 10%. What can you say about the amount borrowed at 10%. What is the solution if the amount borrowed at 10% is $5000c. Suppose the bank sets a maximum of $10,000 at the lowest interest rate of 8%. Is a solution possible that still meets all of the original conditions?d. Explain why 10,000 at 8%, 8000 at 9%, and 7000 at 10% is not a feasible solution for part c55. An animal breeder can buy four types of food for Vietnamese pot-bellied pigs. Each case of Brand A contains 25 units of fiber, 30 units of protein, and 30 units of fat. Each case of Brand B contains 50 units of fiber, 30 units of protein, and 20 units of fat. Each case of brand C contains 75 units of fiber, 30 units of protein, and 20 units of fat. Each case of brand D contains 100 units of fiber, 60 units of protein, and 30 units of fat. How many cases of each should the breeder mix together to obtain a food that provides 1200 units of fiber, 600 units of protein, and 400 units of fat? ................
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