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  Suppose that you start a businessmanufacturing  and selling bicycles, andit costs you $5000 to get started. You determine that each bicycles will cost$400 to manufacture. Explain why the linear equation y1 = 400x 5000 gives your total cost to manufacture x bicycles(y1 in dollars).

31.  You decide to sell each bike for $600. Whatexpression in x represents the revenue you will take in if you sell x bikes ?Write an equation using y2 to express your revenue when you sell x bikes (y2 indollars).

32.  Form a system from theequation in Exercise 30 and 31, and then solve the system assuming y1 = y2,that is cost = revenue.

33.  The value of x fromexercise 32 is the number of bikes it takes to break even. Fill in the blanks:When _25___bikes are sold, the break–even point is reached. At  that point,you have spent __15,000___dollarsand taken in _15,000_____dollars.

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41.  The line segment has an equation that can bewritten in the form y = ax b. Using the coordinates of point P with x=  1996 and y  = 1339, write an equation in variables a andb.

42. Using thecoordinates of p Q with X = 2004 and y = 1536 write a second equation in thevariable of a and b

43. Writethe system of equations formed from the two equations in Exercises 41

and 42, and solve the system using the eliminationmethod.

45.  Let x = 2002 in the equation of Exercise44, and solve for y to the nearest tenth.

How does the result compare with the actual figureof 1639 million?

46. The actual datapoints for the years 1996 through 2004 do not lie in a perfectly

straight line. Explain thepitfalls of relying too heavily on using the equation in

Exercise 44 to predict attendance.