help me with this word problem?

Question

A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific calculators and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 loss, but each graphing calculator produced a $5 profit, how many of each type should be made daily to maximize net profits?

Answer 1

 

let consider

 

number of scientific calculators produced=x
number of graphing calculators produced=y

 

First we shd finf constraints

 

1) Long-term projections indicate an expected demand of at least 100 scientific calculators and 80 graphing calculators each day

x>=100

y>=80

 

2) Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily.

x<=200

y<=170

 

3)To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. 

x+y>=200

 

Now we can write profit as function

 

Profit =-2x+5y

 

So P=-2x+5y

 

constraints

 

100<=x<=200
80<=y<=170

x+y>=200

 

you have to graph these 3 equations and find feasibility region

and test the corner of feasibility region to maximize profit

 

After graphing this I got the corner points at

 (100, 170)

(200, 170)

(200, 80)

(120, 80)

(100, 100)

 

 maximum value of P = 650 at (x, y) = (100, 170).

so

100 scientific calculators and 170 graphing calculators