Linear Programming: units of paper produced for max. profits

[mhmdndoye]

The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can produce at most 200 units of paper a day. At least 10 units of notebook paper and 80 units of newspaper are required daily by regular customers. If the profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350. How many units of paper should the manager have the mill produce each day to maximize profits?


I really need help on making a sytem of inequalities!!! I just need a guide to find the answer, please

 

[mhmdndoye]

The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can produce at most 200 units of paper a day. At least 10 units of notebook paper and 80 units of newspaper are required daily by regular customers. If the profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350. How many units of paper should the manager have the mill produce each day to maximize profits?

I cannot get what I have to add in order to find the number papers. I also cannot understand why my calculations are not working.

x= number of notebooks
y= number of newsprint

( x + y < 200 )-80
10x + 80 y > 850

-70x > -16000 ?
x > 228.57

It does not make sense! :?

 

[arthur ohlsten]

Re: Linear Programming

If the profit on notebook paper = $500 a unit
if the profit on newsprint = $350 a unit

produce as much notebook paper as possible and a minimum of newsprint
minimum newsprint = 80 units answer
total units produced 200 units answer
notebook units = 200-80 = 120

profit = 500[120 ]+ 350[80] in dollars
profit = 60,000+28,000= $ 88,000

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....................................... BY CALCULUS...............................

let P = amount notebook paper 10<P
let n = amount newsprint 80<n

profit[$]=500p+350n
P+n=200 or
n=200-p substitute

profit = 500[p]+350[200-p]
profit = 500p+70000-350p
profit =150p +70,000
take derivative with respect to p and set =0
d[profit]/dp =150

the profit increase with p, thus make maximum quantity of p, or 200 - minimum amount of n
p=200-80
p=120 answer
n=80 answer

Arthur

the profit decreases wit p, so make p a minimum
Arthur

 

[Deleted member 4993]

Re: Linear Programming

The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can produce at most 200 units of paper a day. At least 10 units of notebook paper and 80 units of newspaper are required daily by regular customers. If the profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350. How many units of paper should the manager have the mill produce each day to maximize profits?


I really need help on making a sytem of inequalities!!! I just need a guide to find the answer, please

Please show us your work - indicating exactly where you are stuck - so that we know where to begin to help you.

 

[stapel]

The Northern Wisconsin Paper Mill can convert wood pulp to either notebook paper or newsprint. The mill can produce at most 200 units of paper a day. At least 10 units of notebook paper and 80 units of newspaper are required daily by regular customers. If the profit on a unit of notebook paper is $500 and the profit on a unit of newsprint is $350. How many units of paper should the manager have the mill produce each day to maximize profits?

Using the variables you have defined:

. . . . .x > 0, y > 0 (the usual constraints)

...are superceded by:

. . . . .min. individual production: x > 10, y > 80

. . . . .max. total produced: x + y < 200

. . . . .profit P = 500x + 350y

( x + y < 200 )-80
10x + 80 y > 850

-70x > -16000 ?
x > 228.57

It does not make sense! :?

No, it doesn't.... It might help if you clearly stated your reasoning...?

Eliz.