Calculus problem (demand funnction)

[haris123]

1. In all of this question assume the cost to produce and sell every 100 units of a product is $ 30 and that the demand function is p =100/ (root q) dollars per 100 units, where p; q > 0

(a) State the profitt function, F (q).

(b) Calculate the absolute maximum profit and the level of production at which the maximum profit occurs under the extra assumption that q belongs to [3; 8]

 

[gb7nash]

What do you have so far?

 

[haris123]

What do you have so far?

i knw that the to find the profit we need revenue minus cost. so i think it should be price times q which should be 100root q - 30 ? I am not sure if this is the correct profit function

 

[gb7nash]

i knw that the to find the profit we need revenue minus cost. so i think it should be price times q which should be 100root q - 30 ? I am not sure if this is the correct profit function

Alright, first let's determine what our revenue equation is and cost equation is.

First off, what's the general equation for revenue? (ignoring the question) Once you know that, look at the problem and tell me what revenue is.

Second, remember that the cost is not constant. For every 100 units, it's costing 30 dollars. For example, if I produce 100 units, it costs 30 dollars. If I produce 200 units, it's costing 60 dollars. What kind of relationship is this? How can I make an equation for the cost?

 

[haris123]

Alright, first let's determine what our revenue equation is and cost equation is.

First off, what's the general equation for revenue? (ignoring the question) Once you know that, look at the problem and tell me what revenue is.

Second, remember that the cost is not constant. For every 100 units, it's costing 30 dollars. For example, if I produce 100 units, it costs 30 dollars. If I produce 200 units, it's costing 60 dollars. What kind of relationship is this? How can I make an equation for the cost?

cost changes for every unit - average cost varies. that's the marginal cost which changes for every unit of good produced. in this case its 30 for 100 units. so i would multiply the quantity (q)times the demand function minus the cost which is 30. what do you think?

 

[gb7nash]

cost changes for every unit - average cost varies. that's the marginal cost which changes for every unit of good produced. in this case its 30 for 100 units. so i would multiply the quantity (q)times the demand function minus the cost which is 30. what do you think?

I don't follow this. Here's an easier way of thinking of it:

Draw a vertical axis for cost and horizontal axis for units. Plot the two points I mentioned in the previous post. Draw a line through the two points. What is the equation of this line?

 

[haris123]

I don't follow this. Here's an easier way of thinking of it:

Draw a vertical axis for cost and horizontal axis for units. Plot the two points I mentioned in the previous post. Draw a line through the two points. What is the equation of this line?

you mean the demand function? its 100/ root q

 

[gb7nash]

you mean the demand function? its 100/ root q

I'm talking about the cost.

 

[haris123]

I'm talking about the cost.

cost is 30$ per 100 units

 

[gb7nash]

cost is 30$ per 100 units

Yes...so what is the equation for cost in terms of quantity? C = ____

 

[haris123]

Yes...so what is the equation for cost in terms of quantity? C = ____

there is no equation lol. thts what the question says.

 

[gb7nash]

I think you're misunderstanding the problem, or I'm misunderstanding from the way you typed it:

assume the cost to produce and sell every 100 units of a product is $ 30

This says that for every 100 units you make, it costs 30 dollars. If I make 300 units, it will cost me 90 dollars. The cost is not constant. Does the actual problem say it's constant?

 

[haris123]

I think you're misunderstanding the problem, or I'm misunderstanding from the way you typed it:



This says that for every 100 units you make, it costs 30 dollars. If I make 300 units, it will cost me 90 dollars. The cost is not constant. Does the actual problem say it's constant?

no it doesn't say its constant. however it would be wrong to assume that the cost for producing 300 units would be 90. that's the theory of marginal cost. it changes with every unit produced. if you are assuming that it doesnt. does it help to find the solution?
here is the link to the direct question. ( http://www.math.utsc.utoronto.ca/a32f/A32_exam_fall_2007.pdf) page 6 question no 1

 

[gb7nash]

I think you're thinking of variable cost, not marginal cost. It's been awhile since I've dealt with marginal cost, but the definition is the change in total cost if the quantity produced changes by one unit. Marginal cost doesn't play into the calculation of profit. The equation for profit is:

Profit = Revenue - Total Cost,

where Total Cost = Fixed Cost + Variable Cost

There is no fixed cost from the problem, so:

Fixed Cost = 0.

What we're looking for here is the variable cost.

 

[haris123]

I think you're thinking of variable cost, not marginal cost. It's been awhile since I've dealt with marginal cost, but the definition is the change in total cost if the quantity produced changes by one unit. Marginal cost doesn't play into the calculation of profit. The equation for profit is:

Profit = Revenue - Total Cost,

where Total Cost = Fixed Cost + Variable Cost

There is no fixed cost from the problem, so:

Fixed Cost = 0.

What we're looking for here is the variable cost.

so what do you think is the profit function?

 

[haris123]

i still don't get it.

 

[HallsofIvy]

there is no equation lol. thts what the question says.

No reason to LOL- the problem does not give an equation directly, that's why gb7nash asked you for one. If it cost $30 to produce 100, how much does it cost to produce 1? How much does it cost to produce "x" of them?

Now, I have a question- what, exactly, do the variables "p" and "q" represent? Normally, "p" stands for "price" and "q" for "quantity sold" but your equations look like you have that backwards.