SOLUTION: A company makes two chemicals:type1 and type 2. Due to storage problems, a miximum of 100 pounds of type 1 and 150 pounds of type 2 can be mixed and packaged each year. One pound o

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A company makes two chemicals:type1 and type 2. Due to storage problems, a miximum of 100 pounds of type 1 and 150 pounds of type 2 can be mixed and packaged each year. One pound o      Log On


   

Question 117258This question is from textbook
: A company makes two chemicals:type1 and type 2. Due to storage problems, a miximum of 100 pounds of type 1 and 150 pounds of type 2 can be mixed and packaged each year. One pound of type 1 takes 60 hours to mix and 70 hours to package; one pound of type 2 takes 40 hours to mix and 40hours tp package.The mixing department has at most 7200 hours available each year and packaging has at most 7800 hours available. If the profit for one pound of type 1 is $62and for one pound type 2 is $40, what is the maximum profit possible each year? This question is from textbook

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A company makes two chemicals: type 1 and type 2. Due to storage problems, a maximum of 100 pounds of type 1 and 150 pounds of type 2 can be mixed and packaged each year. One pound of type 1 takes 60 hours to mix and 70 hours to package; one pound of type 2 takes 40 hours to mix and 40 hours to package.The mixing department has at most 7200 hours available each year and packaging has at most 7800 hours available. If the profit for one pound of type 1 is $62 and for one pound type 2 is $40, what is the maximum profit possible each year?
:
Let x = amt of type 1; y = amt of type 2
:
Storage constraints
x =<100
y =<150
:
Mixing constraint:
60x + 40y =<7200
40y = 7200-60x; arrange in the y=mx +b form
y = 180 - 1.5x; divided equation by 40
:
Packaging constraint:
70x + 40y =< 7800
40y = 7800 - 70x
y = 195 - 1.75x
:
Plot all 4 of these equations:
:

:
Area of feasibility:
At or below the horizontal line
At or left of the vertical line
At or below the lowest slanted line
:
The objective functions for each corner of the region
solve:
60x+40y = 7200
70x+40y = 7800
Results:
x=60,y=90
62(60) + 40(90) =
3720 + 3600 = 7320
:
Solve:
70x+40y = 7800
x = 100
Results:
x=100,y=20
62(100) + 40(20) =
6200 + 800 = 7000
:
solve:
60x+40y = 7200
y = 150
results
x=20,y=150
62(20) + 40(150) =
1240 + 6000 = 7240
:
Max profit would be 60 type 1 and 90 type 2