Maximizing Profit: 1750 TVs sell in one week @ $540 each

[mrderson]

A manufacture has been selling 1750 television sets a week at $540 each. A market survey indicates that for each $14 rebate offered to a buyer, the number of sets sold will increase by 140 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price.
p(x)=.1+715

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
=182.5

c) If the weekly cost function is 157500 + 180 x, how should it set the size of the rebate to maximize its profit?

I did part A and B but i don't know how to do c.
I thought that you would plug something into 157500+180x but i don't know what.
I would be so grateful if someone could tell me how to do part c.





** Its not a typo that P(x) is twice
** I can't remember, i started this problem like a week ago in my class and i don't have the notes, sorry... i think that i made an equation out of the numbers at the top... (I can't remember what it was) then i found the derivative and set it equal to 0. sorry i can't remember more of what i did, i just need to know what i do with the equation in part c, if you know...

 

[Deleted member 4993]

Re: Maximizing Profit

A manufacture has been selling 1750 television sets a week at $540 each. A market survey indicates that for each $14 rebate offered to a buyer, the number of sets sold will increase by 140 per week.

a) Find the function representing the demand p(x), where x is the number of the television sets sold per week and p(x) is the corresponding price.

Is there a typo here? Demand function and price function - both expressed as p(x)??

p(x)=.1+715 <<< how is this a function of 'x'?

b) How large rebate should the company offer to a buyer, in order to maximize its revenue?
=182.5 <<< How did you calculate this?

c) If the weekly cost function is 157500 + 180 x, how should it set the size of the rebate to maximize its profit?

How is profit calculated from revenue and cost?


I did part A and B but i don't know how to do c.
I thought that you would plug something into 157500+180x but i don't know what.
I would be so grateful if someone could tell me how to do part c.