SOLUTION: A company invests in a project and it has been estimated that after x months of running, the cumulative profit (€000) for the project is given by the function -3x(squared) + 31.5x
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Question 1131750: A company invests in a project and it has been estimated that after x months of running, the cumulative profit (€000) for the project is given by the function -3x(squared) + 31.5x - 60, where x represents time in months. The project can run for nine months at the most.
I. Draw a graph which represents the profit function
2. Calculate the breakeven point
3. What is the initial cost of the project?
4. Use the graph to estimate the best time to end the project.
5. Etimate the profit or loss at 1.5months
6. Estimate the months where there will be a profit of €10,000 Answer by greenestamps(13198) (Show Source):
A graph, showing the profit function (red) and (for part 6) where the profit is 10000 (green)...
Use your graphing calculator....!
(1) graph the function (a good window is -10 to 10 by -10 to 30)
(2) breakeven point(s) -- where the profit function is 0; estimate or use your graphing calculator
(3) initial --> x=0; evaluate the function at x=0. Since the revenue is initially 0, the initial cost is -P(0). (You could use your graphing calculator to evaluate P(0); but it's easier just to evaluate P(0) by looking at the function)
(4) best time to end: when the profit is maximum (find vertex of the parabola using your calculator)
(5) profit at 1.5. months: estimate, or evaluate P(1.5) using your calculator
(6) graph P(x)=10 (green line on graph) along with the profit function and find where they intersect (estimate or use your graphing calculator)
