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Quadratic Function Model

Annual profit in thousands of dollars is given by the function, P(x) = -.1x2 + 50x - 300, where x is the number of items sold, x ? 0.

Describe the meaning of the number -.1 in the formula, in terms of its meaning in relation to the profit.
Describe the meaning of the number -300 in the formula, in terms of its meaning in relation to the profit.
Find the profit for 5 different values of x
Graph the profit function over its given domain; use the 5 values calculated in part 3 to construct the graph and connect these points with a smooth curve In Excel or another graphing utility. Insert the graph in a Word file and attach the graph in a Word file to the class DB thread.
Will this profit function have a maximum, if so, what is it?
What steps should the company take to prepare for your answer to part 5?
Post your final draft as a response to this post; use the small group area for collaboration.

Solution Preview

See the attached file.

-.1 in the equation is the coefficient that is multiplied to the square of the number of items sold. This term will reduce the profit by a factor of .1 for the square of every item sold, and can be attributed as a factor that deducts a small portion of profit for selling each item.

-300 in the formula is a constant, which is a representation ...

Solution Summary

Quadratic function models are examined in the solution. The profits for the different values are determined.

$2.19