Question 612054: I am having troubles with these problems, I have never had Algebra before now and I am finding it very hard to understand, I have been out of school for 34 years now, so this is kinda hard for me. here is are the problems I need help with.
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.
1.describe the meaning of the number -.1 in the formula, in terms of its meaning in relation to the profit.
2.describe the meaning of the number -300 in the formula, in terms of its meaning in relation to the profit.
3.find the profit for 5 different values of x
4.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.
5.will this profit function have a maximum, if so, what is it?
6.what steps should the company take to prepare for your answer to part 5?
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! 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.
1.describe the meaning of the number -.1 in the formula, in terms of its meaning in relation to the profit.
The high order term will, as x gets increasingly large, dominate the result. The fact that coefficient of that term is negative (-0.1) says that at some point making more units will result in less profit. So that number says that at some point, we will need o stop making units.
2.describe the meaning of the number -300 in the formula, in terms of its meaning in relation to the profit.
-300 is the amount of 'profit' (a loss) that you had to incur before producing anything. think of it as your start up costs. Now you need to make units in order to cover those costs and then, eventually, make a profit
3.find the profit for 5 different values of x
Just pick 5 values for x, and plug them in and solve. How about 50, 100, 200, 250, and 300 ?
4.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.
On you. plug and play :)
5.will this profit function have a maximum, if so, what is it?
Yes it will. You can look at your graph and see. (250) numbers on either side of 250 will result in lower profit.
6.what steps should the company take to prepare for your answer to part 5?
They had better figure out if they want to maximum profit or maximize some other measure (revenue perhaps). Many businesses might decide to make fewer or more units than what would maximize profit because they value some other measure more than the money. Few would operate at a loss, but some may not be able to make 250 units. Or they might be able to make 270 and desire to keep their staff fully employed rather than cutting them back on hours or laying them off. that type of thing
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