Question

Sometimes calculating a business profit requires using a quadratic function. Think about how the problems presented below might involve a quadratic and how it could involve a business calculation.

People frequently need to calculate the area of rooms, boxes or plots of land. An example might involve building a rectangular lawn or room where one side must be twice or three times the length of the other side. For example, if you have to paint the room or lay down wood on the floor of the room or do some other work, with this information, you can create an equation for the area of the room using the ratio of the two sides. Provide some examples or work you would do and what type of business calculation.

How would set up the equation for this problem?

Answer 1

A quadratic equation looks like this ax2 + bx + c = 0 Quadratic equations are actually used in everyday life, as when calculating areas, determining a product's profit A frequent calculation of area of rooms, boxes or land is required. Example, if only 4 square foot of wood is available to use for bottom of the box, an equation can be created for the area of the box using the ratio of the two sides. This means the area, the length times the width, in terms of x would equal x times 2x, or 2x^2. This equation must be less than or equal to four to successfully make a box using these constraints. Sometimes calculating a business profit requires using a quadratic function. If a businessman wants to sell something – even something as simple as lemonade – he needs to decide how many items to produce so that there's a profit. Let's say, for example, that he's selling glasses of lemonade, and he wants to make 12 glasses. He knows, however, that he'll sell a different number of glasses depending on how he sets the price. At $100 per glass, he's not likely to sell any, but at $0.01 per glass, he'll probably sell 12 glasses in less than a minute. So, to decide where to set the price, use P as a variable. The estimated demand for glasses of lemonade be at 12 - P. The revenue, therefore, will be the price times the number of glasses sold: P times 12 minus P, or 12P - P^2.