SOLUTION: Graph each system of constraints. Find all vertices. Evaluate the objective function at each vertex to find the maximum or minimum value. 1)x<3 y<7 x>0,y>0 maximum for p=2x+

Question 309378: Graph each system of constraints. Find all vertices. Evaluate the objective function at each vertex to find the maximum or minimum value.
1)x<3
y<7
x>0,y>0
maximum for p=2x+3y

2) 2x+y<30
x+y<20
x>0, y>0
minimum for c=x+4y

3. Jerome burns 4 cal/min walking and 10 cal/min running. He walks between 10 and 20 min each day and runs between 30 and 45 min each days. He never spends more than an hour running and walking together. How much time should he spend on each activity to maximize the number of calories he burns?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1)P(X,Y)=2X+3Y

P(0,0)=0+0=0
P(0,7)=0+3(7)=21
P(3,0)=2(3)+0=6
P(3,7)=2(3)+3(7)=27
The max occurs at (3,7).
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2)C(X,Y)=X+4Y

C(0,0)=0+0=0
C(0,20)=0+4(20)=80
C(15,0)=15+0=15
C(10,10)=10+4(10)=50
The min occurs at (0,0).
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Let C(X,Y) be the calories burned walking X minutes and running Y minutes.
C(X,Y)=4X+10Y
Constraints: 10<=X<=20, 30<=Y<=45.
1)C(X,Y)=4X+10Y

C(10,30)=4(10)+10(30)= 340
C(10,45)=4(10)+10(45)=490
C(20,30)=4(10)+10(30)=380
C(20,45)=4(10)+10(45)=530
The max occurs at (10,45).
10 minutes walking, 45 minutes running.
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