Central High School has $60,000 to spend on computers and other stuff, so its budget equation is C + X = 60, 000, where C is expenditure on computers and X is expenditures on other things. C.H.S. currently plans to spend $20,000 on computers. The State Education Commission wants to encourage “computer literacy” in the high schools under its jurisdiction. The following plans have been proposed.
Plan A: This plan would give a grant of $10,000 to each high school in the state that the school could spend as it wished.
Plan B: This plan would give a $10,000 grant to any high school, so long as the school spent at least $10,000 more than it currently spends on computers. Any high school can choose not to participate, in which case it does not receive the grant, but it doesn’t have to increase its expenditure on computers.
Plan C: Plan C is a “matching grant.” For every dollar’s worth of computers that a high school orders, the state will give the school 50 cents.
Plan D: This plan is like plan C, except that the maximum amount of matching funds that any high school could get from the state would be limited to $10,000.
(a) Write an equation for Central High School’s budget if plan A is adopted. C + X = 70, 000. Use black ink to draw the budget line for Central High School if plan A is adopted.
(b) If plan B is adopted, the boundary of Central High School’s budget set has two separate downward-sloping line segments. One of these segments describes the cases where C.H.S. spends at least $30,000 on computers.
This line segment runs from the point (C,X) = (70, 000, 0) to the point
(C,X) = _________.
(c) Another line segment corresponds to the cases where C.H.S. spends less than $30,000 on computers. This line segment runs from (C,X) =
_________ to the point (C,X) = (0, 60, 000). Use red ink to draw these two line segments.
(d) If plan C is adopted and Central High School spends C dollars on computers, then it will have X = 60, 000 − .5C dollars left to spend on other things. Therefore its budget line has the equation . _________.
Use blue ink to draw this budget line.
(e) If plan D is adopted, the school district’s budget consists of two line segments that intersect at the point where expenditure on computers is _________ and expenditure on other instructional materials is _________.
(f) The slope of the flatter line segment is −.5. The slope of the steeper segment is −1. Use pencil to draw this budget line.