Question

Your computer supply store sells two types of laser printers. The first type, A, has a cost of $86 and you make a $45 profit on each one. The second type, B, has a cost of $130 and you make a $35 profit on each one. You expect to sell at least 100 laser printers this month and you need to make at least $3850 profit on them. How many of what type of printer should you order if you want to minimize your cost?

Answer 1

can you mix and match A and B or is it just one or the other.

Answer 2

you can mix and match

Answer 3

if you want to minimize cost, then you probably want to use type A.

Answer 4

can you explain what the equation would look like you dont need to answer it though i would like to try it on my own

Answer 5

Is this multi-variable calculus?

Answer 6

yes

Answer 7

the text book i have did not get into lagrange multipliers yet so no

Answer 8

ok, well we know that printer A will always be a better deal. the cost is lower and the profit is higher. you will reach your profit goal quicker with a lower cost

Answer 9

ok

Answer 10

therefore, just buy 100 type A printers and you meet the 100 printer requirement, you meet the profit requirement, with the lowest cost.

Answer 11

k

Answer 12

my method is more intuitively based, but I think it would be better for you if @wio could step you through how to do this using calculus.

Answer 13

Honestly I need to know what formulas or the topic of the chapter for the homework you are doing to help you.

Answer 14

This is looking a lot like a linear progranming problem. \[\begin{array}{rcl}
f(x,y) &=& 86x+130y \\
45x+35y &\geq& 3850 \\
x+y &\geq& 100
\end{array}
\]

Answer 15

there is no certain name it is just in the middle of the chapter but the equation you gave me seemed to work.

Answer 16

@sloths help me with this problem

Answer 17

is it multiple choice?