Question

Q1:

A company produces a special new type of TV. The company has fixed costs of ​$458 comma 000458,000​, and it costs ​$1200 to produce each TV. The company projects that if it charges a price of ​$2600 for the​ TV, it will be able to sell 700 TVs. If the company wants to sell 750 ​TVs, however, it must lower the price to ​$2300. Assume a linear demand. If the company sets the price of the TV to be ​$3800, how many can it expect to​ sell?

It can expect to sell ____ TVs

​(Round answer to nearest​ integer.)

Q2:

A company produces a special new type of TV. The company has fixed costs of ​$483,000​, and it costs ​$1000 to produce each TV. The company projects that if it charges a price of ​$2600 for the​ TV, it will be able to sell 800 TVs. If the company wants to sell 850 ​TVs, however, it must lower the price to ​$2300. Assume a linear demand. If the company sets the price at ​$3800​, how much profit can it​ earn?

It can expect to​ earn/lose $____.

​(Round answer to nearest​ dollar.)

Q3:

A beverage company produces bottled water. Each bottle costs the company ​$0.03 to​ produce, and the company has fixed costs of $2800 each week. If the company sells the bottled water for $1.25 per​ bottle, what profit does the company earn by producing and selling 4600 bottles of water in a​ week? What is the profit earned by selling 4600 ​bottles? The profit​ (or lose) is ​$_____.  

Round to the nearest cent.

Q4:

A company sells doorknobs at a price of ​$12.75. A doorknob costs the company ​$2.50 to​ produce, and the company has fixed costs of ​$1500 each month. If the company can only afford $2400 in costs this​ month, how many doorknobs can it ​produce?

It can afford to produce ______ doorknobs this month.

​(Round to the nearest​ integer.)

I'm sorry for posting 4 questions but I don't have any more left and it's very urgent. Please help! Thank you.

Answer 1

Q.1.

As mentioned, let us assume a linear demand function for this TV.

(Linear demand function implies inverse linear demand function i.e. P as a function of Q). Inverse demand function can be written as:

Company projects that at a price of ​$2600 for the​ TV, it will be able to sell 700 TVs.

Also, if company wants to sell 750 ​TVs, it must charge the price to be ​$2300.

Subtracting (2) from (1), we get:

Plugging the value of b to equation 1, we get:

After obtaining values for a and b, we can write inverse demand curve as:

Thus if the company sets the price of the TV to be ​$3800, quantity it sells is:

Q.2.

Following as in question 1, let us assume the following inverse demand function:

Company projects that at a price of ​$2600 for the​ TV, it will be able to sell 800 TVs.

Also, if company wants to sell 850 ​TVs, it must charge the price to be ​$2300.

Subtracting (2) from (1), we get:

Plugging the value of b to equation 1, we get:

After obtaining values for a and b, we can write inverse demand curve as:

Thus if the company sets the price of the TV to be ​$3800, quantity it sells is:

Hence total revenue:

Total cost function is:

Hence profit made by company is:

Q.3.

Total cost function is:

If 4600 bottles are sold at a fixed price of $1.25 per bottle, cost of producing them is:

Hence the loss incurred here is

Q.4.

Total cost function is:

Given that company can only afford a total cost of $2400 this month, hence the maximum quantity of doorknobs that can be produced is: