A company manufactures and sells x smartphones per week. The weekly price-demand and cost equations are p=500−0.5x and C(x)=20,000+135x respectively. a. What price should the company charge for the phones and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue ?
b. What is the maximum weekly profit ? How much should the company charge for the phones, and how many phones should be produced to realize the maximum weekly profit ?

a)

revenue = x amount of phones x price

revenue = x(500 - 0.5x)

revenue = 500x - 0.5x²

we find revenue' (derivative):

revenue' = 500 - x

x = 500

the company should sell 500 smartphones to maximize revenue, the selling price = 500 - (0.5 x 500) = $250 per smartphone. Maximum weekly revenue = $250 x 500 = $125,000

b)

profit = revenue - cost

profit = 500x - 0.5x²  - 20,000 - 135x

profit = -0.5x² + 365x - 20,000

we must find profit' (derivative):

profit' = -x + 365

x = 365

In order to maximize profits, you have to sell 365 smartphones per week. Maximum weekly profit = -0.5(365²) + 365(365) - 20,000 = -66,612.50 + 133,225 - 20,000 = $46,612.50.

The smartphone's price = 500 - (0.5 x 365) = $317.50

1   all nations face the problem of scarcity because there are limited resources and unlimited wants. nations do not have enough factors of production to produce everything that their population wants. entrepreneurial resources initiate businesses to make new goods and services; labor resources produce goods and services.

2 there are four factors of production: natural resources, labor resources, capital resources, and entrepreneurial resources. natural resources are raw materials from nature that are used to produce goods. trees, water, and grains are natural resources. some natural resources, such as wheat and cattle, are renewable

3 wants

things that you do not need to have in order to survive, but would like to have

needs

things that you must have in order to survive

goods

physical products

services

tasks that a business perform for customers

resources

items that people can use to make or obtain what they need or want

determine

to settle or decide by choice of alternatives or possiblities

4 i really dont know

answer; tech (a) is correct;