week 9- precalc 11

This week in math we learned how to solve a word problem for quadratic functions. The following is an example:

A TV company sells TVs for $400. At thatĀ price, they can sell 500 per week, the company predicts thatĀ for every $50 increase in price, they will sell 20 fewer TVs. what price for a TV will maximize the revenue?

The first step is come up with figure out what formula to use based on the vocabulary used in this case you would use the formula to figure out revenue

Revenue=(price)(#of sales)

R=(400+50x)(500-20x)

The next step is to foil this equation

R=-1000x^2+17000+200,000

Next, you have to get the function to vertex form by completing the square

R=-1000(x^2-17+\frac{289}{4}-\frac{289}{4})+200,000

Then factor and add

R=-1000(x-\frac{17}{2})^2+272,250

Vertex:(8.5,272,250)

Now you know that to maxamize revenue they can increase the price 8.5 times for and increase in profit of $72,250

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