Math for Social SciencesExam 1 (Problems 1-5) A company wants to make and sell computers. It takes an initial investment of $50,000 to setup a factory to produce the computers, and an additional cost $200 per computer to produce each computer. The company plans to sell the computers at a price of $500 per computer.1. What is the Cost function?a. C(x)=500x b. C(x) = 50,000x +200 c. C(x)=500x+50,000 d. C(x)=200x+500e. None of the previous2. What is the Revenue function?a. R(x)=200x b. R(x)=500x c. R(x)=300x-50,000 d. 200x+50000 e. None of the previous3. What is the Profit function?a. P(x)=200x b. P(x)=500x c. P(x)=300x-50,000 d. 300x+50000 e. 700x-50,0004. What is the break even point?a. 66 computers b. 160 computers c. 60 computers d. 167 computers e. 96 computers5. How much profit (or loss) will the company make by selling 100 computers?a. $20,000 loss b. $20,000 gain c. $30,000 loss d. $30,000 gain e. None of the above(Problems 6-10) For the function2122232242)(xxxxxxxf6. f(-4)=a. 12 b. -11 c. 32 d. -5 e. -207. f(-1)=a. 31 b. -3 c. -5 d. 1 e. -1 8. f(5)=a. 21 b. -11 c. 31 d. -5 e. 319. f(-2)=a. -7 b. -8 c. 0 d. 1 e. -210. f(2)=a. 0 b. 1 c. 31 d. 32 e. 3(Problems 11-15) Let P = (-1,-1) and Q = (1,3) be points. Let L1 represent the straight line that passes through the points P & Q.11. Determine the slope between the points P and Q.a. 1 b. 2 c. -2 d. 3 e. -312. Determine the equation of the line L1 between the points P and Q.a. y=2x+1 b. y= -2x-1 c. y=3x+1 d. y= -2x+1 e. y=x-213. Determine the slope of a line that is parallel to L1.a. -½ b. -1 c. -2 d. -3 e. 2 14. Determine the equation of a line that passes through the point (0,2) and is parallel to L1.a. y= -4x+1 b. y= -½x-2 c. y=2x+2 d. y=4x-2 e. y=2x+1 15. Determine the slope of a line that passes through the points P and (1,-5)a. 4 b. -4 c. ½ d. -½ e. -216. Solve for all solutions of the system of equations14232yxyxa. (0,7) b. (2,9) c. (x,2x-5) d. (x, ½ x -3) e. No solution17. Solve for all solutions of the system of equations:22412yxyxa. (1,1) b. (2,3) c. (x,2x-1) d. (x, x-2) e. No solution18. An investor decides to invest a total of $1000 in Stocks, which have an interest rate of 10%, and Bonds, which have an interest rate of 5%. If the investor earned a total of $86.70, then determine the amount money invested in stocks and the amount invested in bonds.a. 166 in bonds and 834 in stocksb. 333 in bonds and 667 in stocksc. 734 in bonds and 266 in stocksd. 566 in bonds and 444 in stockse. None of the above19. The solution to the system of equations 1201313yxzyzyxis:a. (-1,0,0) b. (1,2,3) c. (-2,1,1) d. (x, 2x, 2x-1) e. none of the previous choices20. You wish to make a cocktail, made from a mixture of wine and vodka. Wine contains 10% alcohol, while vodka contains 20% alcohol. You want to make a mixture of 10 liters, in such a way that the final mixture contains only 15.5% alcohol. How much wine and vodka must be used?a. 1L of wine and 9L of vodkab. 4L of wine and 6L of vodka c. 3.5L of wine and 6.5L of vodkad. 4.5L of wine and 5.5 L of vodkae. none of the above(Problems 21-25) Mark A for True. Mark B for False21. A function is a relation between input values (x) and output values (y) in such a way that it ispossible for two x coordinates with the same y coordinate.22. A function is a relation between input values (x) and output values (y) in such a way that it ispossible for two y coordinates with the same x coordinate.23. If two lines L1 and L2 are perpendicular, then the slopes of the two lines are equal.24. A linear system of equations with three variables can have no solution, one solution, two solutions, or infinite solutions.25. A linear system of equations of two variables can have no solution, one solution, or infinite