Question 309378
1)P(X,Y)=2X+3Y
{{{ drawing( 300, 300, -5, 10, -5,10, grid(1),
circle(3,0,.3),
circle(3,7,.3),
circle(0,7,.3),
circle(0,0,.3),

green(line(0,0,0,7)),
green(line(0,7,3,7)),
green(line(3,7,3,0)),
green(line(3,0,0,0)))}}}
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).
.
.
.
2)C(X,Y)=X+4Y
{{{ drawing( 300, 300, -2, 22, -2,22, grid(1),
circle(15,0,.5),
circle(10,10,.5),
circle(0,20,.5),
circle(0,0,.5),
graph(300,300,-2,22,-2,22,30-2x,20-x),
blue(line(0,0,0,20)),
blue(line(0,20,10,10)),
blue(line(10,10,15,0)),
blue(line(15,0,0,0)))}}}
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).
.
.
.
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
{{{ drawing( 300, 300, -5, 30, -5,50, grid(1),
circle(20,30,.6),
circle(20,45,.6),
circle(10,45,.6),
circle(10,30,.6),

green(line(20,30,20,45)),
green(line(20,45,10,45)),
green(line(10,45,10,30)),
green(line(10,30,20,30)))}}}
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.