30. Suppose that you start a business
manufacturing and selling bicycles, and
it 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. What
expression 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 in
32. Form a system from the
equation in Exercise 30 and 31, and then solve the system assuming y1 = y2,
that is cost = revenue.
33. The value of x from
exercise 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___dollars
and taken in _15,000_____dollars.
41. The line segment has an equation that can be
written in the form y = ax + b. Using the coordinates of point P with x
= 1996 and y = 1339, write an equation in variables a and
42. Using the
coordinates of p Q with X = 2004 and y = 1536 write a second equation in the
variable of a and b
the system of equations formed from the two equations in Exercises 41
and 42, and solve the system using the elimination
45. Let x = 2002 in the equation of Exercise
44, and solve for y to the nearest tenth.
How does the result compare with the actual figure
of 1639 million?
46. The actual data
points for the years 1996 through 2004 do not lie in a perfectly
straight line. Explain the
pitfalls of relying too heavily on using the equation in
Exercise 44 to predict attendance.