You run a small furniture business. You sign a deal with a customer to deliver up to 500 chairs, the exact number to be determined by the customer later. The price will be $110 per chair up to 400 chairs, and above 400, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 400 ordered.

a) What is the largest revenue your company can make under this deal?
R=______ dollars

b) What is the smallest revenue your company can make under this deal?
R=_____dollars

please explain! Thanks:)

Question

You run a small furniture business. You sign a deal with a customer to deliver up to 500 chairs, the exact number to be determined by the customer later. The price will be $110 per chair up to 400 chairs, and above 400, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 400 ordered.

a) What is the largest revenue your company can make under this deal?
R=______ dollars

b) What is the smallest revenue your company can make under this deal?
R=_____dollars

please explain! Thanks:)

hero · Answer

Piecewise Function:


x = number of chairs ordered

f(x) = 110x, if x < 400
      = 110x - .25x if  400 < x < 500

anonymous · Answer

okay:)

so from here, do you set them equal to each other? :/not too sure :(

hero · Answer

Finding maximum and minimum values of the function. You should start off with graphing the function given the ranges

anonymous · Answer

okay... so set it up on a x/y axis? ;/

not sure how to graph this though :(

hero · Answer

You graph each one at a time. You can use a calculator or desmos.com to graph. They are just linear functions anyway. Nothing difficult.

anonymous · Answer

i punched it into wolfram alpha...

is this right? for 110x, if x < 400 ?

anonymous · Answer

but i couldn't get anything from that second function :/

hero · Answer

It is better to use desmos.com to graph because you can set up proper limits for x

hero · Answer

I'm surprised you made it this far without knowing how to graph on a calc.

anonymous · Answer

oh on my graphing calc?

anonymous · Answer

and don't know how to use desmos... never used it before :/

hero · Answer

Yes, you can do it on your graphing calc as well. Hang on a min...

anonymous · Answer

ahh okay:P

yeah i just forget how to enter the domains :/

hero · Answer

https://www.desmos.com/calculator/fzphk6elx4

anonymous · Answer

ohhh okay i see now :)

so what's the next step from here?

hero · Answer

You should be able to calculate the min and max amounts. You can assume that at least one chair will be sold for minimum. 500 chairs for maximum

hero · Answer

So at least $110 for minimum

hero · Answer

f(1) = 110

hero · Answer

Compute f(500) for maximum

anonymous · Answer

f(500)=110(500) 
         =55,000
?

hero · Answer

According to the piecewise function you use 110x - .25x if 400 < x < 500

hero · Answer

f(500) = 110(500) - .25(500)

anonymous · Answer

ohh so 

f(500) = 110(500) - .25(500)
          =55,000 - 125
          =  54, 875
?

hero · Answer

looks right

anonymous · Answer

and so would that be the largest revenue? since it's the max?

anonymous · Answer

and the smallest revenue is 110?

so 54874=max
and 110=min 
?

hero · Answer

I should have used R(x) for the function

hero · Answer

Yes, that should be correct

anonymous · Answer

ahh okay!! yay! So this problem is all complete?! :O

hero · Answer

I would assume so unless there are other questions to answer

anonymous · Answer

no, that's all :)

hehe yay! thanks!!

hero · Answer

The minimum revenue assumes the customer will purchase at least one chair.

anonymous · Answer

ahh okay:)

anonymous · Answer

thank you!! :D

hero · Answer

yw @iheartfood