Solve using the quadratic formula

In summary, the dealership is planning to increase their markup due to inflation. For every $100 increase, there will be one less car sold each month. To find the maximum revenue, the marketing manager must determine the new markup by solving the quadratic equation -100x^2+2000x+480000. The maximum revenue will be achieved when the number of $100 increases is 10, resulting in a maximum revenue of $490,000.
  • #1
Aka
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0
A large dealership had been selling new cars at $6000 over the factory price. Sales have been averaging 80 cars per mouth. Because of inflation, the $6000 markup is going to be increased. The marketing manager has determined that, for every $100 increase, there will be one less car
sold each month. What should the new markup be in order to maximize the revenue?

Let x rep the number of $100 increases
the equation for revenu is (#sold)(price)
so (80-x)(6000+100x)
then, when you expand it its -100x^2+2000x+480 000
next, solve using the quadratic formula
is everything right?

Thanks
 
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  • #2
Why would you find the values of x giving zero profit?

Find the MAXIMUM of the given profit function, not its roots.
 
  • #3
^ok, thanks, so if my work abouve was correct, the answer should be a maximum of 490 000, when x=10
 
Last edited:

Related to Solve using the quadratic formula

1. What is the quadratic formula?

The quadratic formula is a mathematical equation used to solve quadratic equations in the form of ax^2 + bx + c = 0. It is written as x = (-b ± √(b^2 - 4ac)) / 2a.

2. When should I use the quadratic formula?

The quadratic formula should be used when you have a quadratic equation in the standard form and cannot easily factor it. It is also useful when trying to find the roots of a quadratic equation.

3. Can the quadratic formula be used for all quadratic equations?

Yes, the quadratic formula can be used to solve all quadratic equations. However, it is important to note that some equations may have complex solutions.

4. How do I use the quadratic formula to solve an equation?

To use the quadratic formula, simply substitute the values of a, b, and c into the formula and solve for x. Remember to use the correct signs for the ± symbol and simplify the square root if possible.

5. Are there any other methods to solve quadratic equations?

Yes, there are other methods to solve quadratic equations such as factoring, completing the square, and graphing. However, the quadratic formula is the most reliable and efficient method to solve any quadratic equation.

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