Math 156 – D. Nelson Name:
Review for the Midterm Fall 2005
The manager of the Frozen Air Refrigerator factory notices that on Monday it cost the company a total of $25,000 to build 30 refrigerators and on Tuesday it cost $30,000 to build 40 refrigerators.
1. Find the linear equation that gives the total cost of building the refrigerators as a function of the number of refrigerators manufactured.
2. Explain the meaning of the slope of the line you found in problem #1. If you are unable to do problem 1, use the equation . (C represents the total cost and x represents the number of refrigerators manufactured.)
3. Explain the meaning of the y intercept of the line you found in problem #1. If you are unable to do problem 1, use the equation .
4. T Mobile’s Basic cell phone plan charges $19.99 a month for a plan with 60 “free” minutes, and $0.45 for each additional minute. Write an expression for the monthly cost as a function of the number of minutes used, and graph this function over the domain 0<t<120
5. Solve the system of linear equations using elimination.
6. Solve the system of linear equations using substitution.
7. Solve by hand using matrices
8. Describe the three basic types of systems of linear equations. Be sure to say something about the solutions to the systems, graphs in a two variable case, and how you can recognize each type as you are solving the system.
9. Arctic Juice Company makes three juice blends: PineOrange, using 2 quarts of pineapple juice and 2 quarts of orange juice per gallon; PineKiwi, using 3 quarts of pineapple juice and 1 quart of kiwi juice per gallon; and OrangeKiwi, using 3 quarts of orange juice and 1 quart of kiwi juice per gallon. Each day the company has 800 quarts of pineapple juice, and 650 quarts of orange juice, and 350 quarts o kiwi juice available. How many gallons of each blend should it make each day if it wants to use up all supplies?
10. Let , and . Find .
11. Let . Find by using row operations.
12. Solve the system of equations using matrix methods. You may find the inverse anyway you would like, just show it to me once you’ve found it. (Calculator or Formula)
13. Graph the solution to the inequality .
14. Solve graphically: Minimize subject to
BAM Bicycles has two factories making Sport and Custom bicycles, one in Washington and the other in Chili. Producing a bicycle involves two processes: assembly and packaging. The labor-hour requirements and the hourly wages at each factory are summarized in the matrices below.
15. Calculate MN. Convince me that you know how to do it by hand.
16. Calculate NM. Using your calculator is acceptable.
17. Which of these products contains meaningful information? Label the rows and columns and title this matrix.
18. Solve the maximization problem given in the table:
x = y = z = s1 = s2 = P =
19. Your small farm encompasses 100 acres, and you are planning to grow tomatoes, lettuce and carrots in the coming planting season. Fertilizer costs per acres re $5 for tomatoes, $4 for lettuce, and $2 for carrots. Based on past experience, you estimate that each acre of tomatoes will require an average of 4 labor-hours per week, and tending to lettuce and carrots will each require an average of 2 labor-hours per week. You estimate a profit of $2000 for each acre of tomatoes, $1500 for each acre of lettuce, and $500 for each acre of carrots. You can afford to spend no more than $4000 on fertilizer, and your farm workers can supply 500 hours/week. How many acres of each crop should you plant to maximize total profits? In this event do you have any unallocated resources?