APPLICATIONS OF QUADRATIC EQUATIONS

The demand function for the manufacturer of a product is p = f (q) = 1800 - 3q, where p is the price (in dollars) per unit when q units are demanded (per week). Find the level of production that maximizes the total income of the manufacturer and determine this income.

• The level of production must be 200 units to maximizes the total income to $240,000.

• The level of production must be 400 units to maximizes the total income to $280,000.

• The level of production must be 300 units to maximizes the total income to $270,000.

• The level of production must be 400 units to maximizes the total income to $240,000.

The demand function for a line of plastic rules of an office supplies company is p = 1.1 - 0.0002q, where p is the price (in dollars) per unit when consumers demand q units (daily). ). Determine the level of production that will maximize the manufacturer's total income and determine this income.

• The level of production must be 2750 units to maximize the total income to $1,512.50

• The level of production must be 2550 units to maximize the total income to $1,212.50

• The level of production must be 2950 units to maximize the total income to $1,812.50

• The level of production must be 2800 units to maximize the total income to $1,912.50

The demand function for the laptops line of an electronics company is p = 2400 - 6q, where p is the price (in dollars) per unit when consumers demand q units (weekly). Determine the level of production that will maximize the manufacturer's total income and determine this income.

• The level of production must be 220 units to maximize the total income to $280,000.

• The level of production must be 180 units to maximize the total income to $200,000.

• The level of production must be 200 units to maximize the total income to $280,000.

• The level of production must be 200 units to maximize the total income to $240,000.

 A market research company estimates that n months after the introduction of a new product, f(n) thousands of families will use it, where $f\left(n\right)=\frac{14}{9}n\left(12-n\right),\ 0\le n\le12$ Estimate the maximum number of families that will use the product.

• Maximum 54,000 families  will use the product.

• Maximum 56,000 families  will use the product.

• Maximum 6,000 families  will use the product.

• Maximum 58,000 families  will use the product.

Mariana standing on a hill shoots an arrow strainght up. the height h, of the arrow in feet, t seconds after it was released, is described by the function $h=-16t^2+80t+12$  What is the maximum height reached by the arrow? How many seconds after it is released, reaches this height?

• The arrow reaches reaches a maximum height of 112 ft. after 2.5 seconds.

• The arrow reaches reaches a maximum height of 120 ft. after 3.5 seconds.

• The arrow reaches reaches a maximum height of 102 ft. after 1.5 seconds.

• The arrow reaches reaches a maximum height of 122 ft. after 4.5 seconds.

 $R=-3p^2+60p+1060$  is the weekly revenue for a company, where p is the price of the company's product. Use the discriminant to find whether is a price for which the weekly revenue would be $1500.

• Yes, there are two different prices for which the weekly revenue is $1500.

• Yes, there is one price for which the weekly revenue is $1500.

• No, there isn't a price for which the weekly revenue is $1500.

The area of a rectangle is 24 square inches. The perimeter of the rectangle is 24 inches. Write a quadratic equation in standard form using w as variable and find the dimensions of the rectangle.

•  $w^2-12w+24=0,\ 3in.\ x\ 8\ in.$  

•  $w^2+12w+24=0,\ 6in.\ x\ 4\ in.$  

•  $w^2-12w-24=0,\ 3in.\ x\ 8\ in.$  

•  $w^2-10w+24=0,\ 4in.\ x\ 6\ in.$  

Mariana standing on a hill shoots an arrow strainght up. the height h, of the arrow in feet, t seconds after it was released, is described by the function    $h=-16t^2+80t+12$   
  How long would the arrow go before it hit the ground?

• About 0.14 seconds

• About 12.45 seconds

• About 14.65 seconds

• About 13.23 seconds

 $p=-0.1x+55$  is price-demand function of a company where p is the price and x the number of units. Find the number of items sold that will give the maximum revenue and what is maximum revenue.

• There is a maximum revenue of $7500.50 when 272 units are sold.

• There is a maximum revenue of $7362.50 when 250 units are sold.

• There is a maximum revenue of $7562.50 when 275 units are sold.

• There is a maximum revenue of $275 when 2275 units are sold.

 $p\left(x\right)=-0.1x^2+43x-3520$  is the profit function of a company where p is the price and x the number of units. How many items should be sold for the company to break even?

• The company should be sold 110 or 320 items to break even.

• The company should be sold 120 or 300 items to break even.

• The company should be sold 0 or 320 items to break even.

• The company should be sold 10 or 120 items to break even.