Question

A store sells bouquets of fruits for $10 a bouquet. The daily cost to produce x bouquets of fruits is defined by the function f(x) = – x 4 + 3x 3 + 5x 2 + 20x + 1.

Answer 1

5

Explanation:

For profit to be had, the selling price (represented by $10x, x being number of bouquets sold) must be greater than the cost to produce (here, -x^4 + 3x^3 + 5x^2 + 20x +1).

Set up an inequality such that 10x is greater than the cost to produce.

10x > -x^4 + 3x^3 + 5x^2 + 20x + 1

-Solving the inequality by subtracting 10x from both sides, we have:

0 > -x^4 + 3x^3 + 5x^2 + 10x + 1

-Using a graphing calculator, (the one they give you on Edgenuity) graph the new function and look for where the graph is below the x axis. (y is less than 0)

Looking at the graph, we see that when x is greater than 0, (you can't sell a negative amount of bouquets) y is greater than 0 up until x = 4.579. After 4.579, the y values become negative. (what we want to be looking at according to the inequality.)

You can't sell 4.579 bouquets, and even if you could, you'd be breaking even, with y=0. The answer isn't 4, because according to the graph and inequality, y would be greater than 0 (making the inequality false). Because of this, we have to find the next whole positive number that would make the inequality true, and that is 5.

Answer 2

5 or C

Explanation:

when you plug in 5, you get -24 as the cost. Then you take that number with the amount of money you make selling 5 flowers and that would be $50 since they are $10/per bouquet. Then when you subtract you get a positive profit of $26.