# Algebra

Hello!

Suppose that the price per unit in dollars of a cell phone production is modeled by
p = \$55 − 0.0125x,
where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R = x · p.
Find the production level that will maximize revenue.

1. 👍 0
2. 👎 0
3. 👁 1,094
1. According to the condition, the revenue (measured in thousands of dollars) is

R(x) = x*(35-0.0125x),

where x is the number of the phones measured in thousand of units.

So, you need to find the maximum of this quadratic function

R(x) = -0.0125x^2 + 35x.

The maximum is achieved at x = -b%2F%282a%29 ( referring to the general form of a quadratic function q(x) = ax%5E2+%2B+bx+%2B+c ),

which at given conditions is x = -35%2F%282%2A%28-0.0125%29%29 = 35%2F0.025 = 1400.

So, the maximum is achieved at the production level 1400 thousand of phone units .

The maximum revenue is the value R(x) at this value of x:

R%5Bmax%5D = R(1400) = -0.0125%2A1400%5E2+%2B+35%2A1400 = 24500 thousands of dollars.

Answer. The maximum revenue is 24500 thousands of dollars achieved at the production level of 1400 thousand of phone units .

1. 👍 0
2. 👎 7

## Similar Questions

1. ### Calculus

The demand function for the Luminar desk lamp is given by the following function where x is the quantity demanded in thousands and p is the unit price in dollars. p = f(x) = -0.1x2 - 0.3x + 39 (a) Find f '(x). f '(x) = (b) What is

2. ### Statistics

Q1:(a) Make a relative frequency table of the data. Enter your answers to three decimal places. Cell Phone Owned Relative Frequency Android smartphone iPhone smartphone Blackberry smartphone Cell phone not smartphone No cell phone

3. ### College Algebra

Suppose that the price per unit in dollars of a cell phone production is modeled by p = \$45 − 0.0125x, where x is in thousands of phones produced, and the revenue represented by thousands of dollars is R = x · p. Find the

4. ### physics

While riding in a hot air balloon, which is steadily descending at a speed of 1.39 m/s, you accidentally drop your cell phone. (a) After 4.00 s, what is the speed of the cell phone? (b) How far is the cell phone below the balloon

1. ### Calculus

The demand function for the Luminar desk lamp is given by p = f(x) = −0.1x^2 − 0.7x + 20 where x is the quantity demanded in thousands and p is the unit price in dollars. (a) Find f '(x). (b) What is the rate of change of the

2. ### math

Suppose the cost function associated with a product is C(x) = cx + F dollars and the revenue function is R(x) = sx, where c denotes the unit cost of production, s the unit selling price, F the fixed cost incurred by the firm, and

3. ### Algebra

Your cell phone plan costs 55 dollars a month, plus 35 cents per minute. Write an equation to represent the monthly bill of the cell phone plan.

4. ### Math

The monthly revenue R (in thousands of dollars) from the sales of a digital picture frame is approximated by R(p) = −10p^2 + 1480p, where p is the price per unit (in dollars). a) Find the unit price that will yield a maximum

1. ### physics

While riding in a hot air balloon, which is steadily descending at a speed of 1.39 m/s, you accidentally drop your cell phone. (a) After 4.00 s, what is the speed of the cell phone? (b) How far is the cell phone below the balloon

2. ### Calculus

A company decides to begin making and selling computers. The price function is given as follows: p=−70x+4000, where x is the number of computers that can be sold at a price of p dollars per unit. Additionally, the financial

3. ### Calculus

The management of the Titan Tire Company has determined that the quantity demanded x of their Super Titan tires/week is related to the unit price p by the relation p = 144 − x^2 where p is measured in dollars and x is measured

4. ### !math (6)

The quantity demanded x (in units of a hundred) of the Mikado miniature cameras per week is related to the unit price p (in dollars) by p = −0.2x^2 + 220 and the quantity x (in units of a hundred) that the supplier is willing to