Question 1195573: Can I please have help with this, Thank you!
Sharon has applied to the navy. She plans to racquetball and cycle to get into shape for the fitness test. Sharon wants to spend no more than 12 hours exercising a week and wants to burn a maximum of 7000 calories. She ahs calculated she will burn 700 calories per hour playing racquetball and 350 calories per hour cycling.
To describe this scenario, what quantities should x and y represent
B. Write a system of inequalities which will represent Sharon’s situation( Hint: three are 4 linear inequalities for this scenario)
C. Graph the system of inequalities, mark the points of intersection of all lines and shade the solution region.
D. Bicycling is free but racquetball costs $20 per hour to play. Write the objective function for this scenario. How much time should she spend on each activity in orde to minimize costs?
E. How much time should she spend on each activity if she just wants to maximize her calorie burn?
The diagram has the line 4x+3y=12 dividing the Cartesian Plane into seven regions. Write a system of inequalities the describes region D.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of hours playing racquetball.
let y = the number of hours cycling.
your inequalities are:
x + y <= 12
this represents the total number of hours she wants to use is less than 12.
700x + 350y <= 7000
this represents the total number of calories she wants to burn.
it's 700 calories per hour times the number of hours for racquetball plus 350 calories per hour times the number of hours for cycling.
x >= 0
y >= 0
this represents that the number of hours for each activity can't be less than 0.
if she wants to minimize costs, then the objective function for costs is:
20x + 0y, which you want to minimize.
this represents 20 dollars per hour for racquetball plus 0 dollars for cycling.
if she wants maximize calories consumed, then the objective function for calories is:
700x + 350y, which you want to maximize.
this represents 700 calories per hour times number of hours for racquetball plus 350 calories per hour times number of hours for cycling.
you can graph this manually, or you can use the calculator at desmos.com.
if you use the calculator at desmos.com, you would:
graph the opposite of the inequalities.
the area of the graph that is not shaded will be your region of feasibility.
the corner points of the region of feasibility will be where your maximum calory burn and your minimum cost will be.
objective function for cost is 20x + 0y
objective function for calories is 700x + 350y
constraint inequalities are:
x + y <= 12
700x + 350y <= 7000
x >= 0
y >= 0
graph the opposite of the inequalities.
identify the corner points.
evaluate the objective functions at the corner points.
the graph looks like this.
the corner points of the feasible region are:
(0,12)
(8,4)
(10,0)
the minimum cost will be at (0,12), where the cost is 20 * 0 + 0 * 12 = 0.
the maximum calorie burn will be at (10,0) or (8,4).
at (10,0), the maximum calorie burn is 10 * 700 = 7000
at (8,4), the maximum calories burn is 8 * 700 + 4 * 350 = 7000.
you have a minimum cost of 0 and a maximum calorie burn of 7000.
i have no idea what the equation of 4x + 3y = 12 represents.
i don't see it as being applicable to this problem, unless there is some other information about the problem that you didn't show.
if you were to manually create the graph, you would do the following.
graph the equations of:
x + y = 12
700x + 350y = 7000
x = 0
y = 0
you would then shade the areas for the inequalities of:
x + y <= 12
700x + 3506 <= 7000
x >= 0
y >= 0
that graph would look like this:
using desmos.com calculator, the region of feasibility is the area that is not shaded.
doing it manually, the region of feasibility is the area that is shaded.
the region of feasibility is the same, whichever way you wanted to graph it.
the corner points are the same and the analysis is the same.
note that, when she minimizes cost, the maximum calorie burn is 12 * 350 = 4200.
this is acceptable since it is less than 7000, which was one of the constraints.
all of the constraints need to be satisfied, not just some of them.
at (0,12), she had exercised for 12 hours which is <= 12 and she had burned 4200 calories which is <= 7000.
at (8,4), she had exercised for 12 hours which is <= 12 and she had burned 7000 calories which is <= 7000.
at (10,0), she had exercised for 12 hours which is <= 12 and she had burned 7000 calories which is <= 7000.
let me know if you have any questions.
theo
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
Can I please have help with this, Thank you!
Sharon has applied to the navy. She plans to racquetball and cycle to get into shape for the fitness test. Sharon wants to spend no more than 12 hours exercising a week and wants to burn a maximum of 7000 calories. She ahs calculated she will burn 700 calories per hour playing racquetball and 350 calories per hour cycling.
To describe this scenario, what quantities should x and y represent
B. Write a system of inequalities which will represent Sharon’s situation( Hint: three are 4 linear inequalities for this scenario)
C. Graph the system of inequalities, mark the points of intersection of all lines and shade the solution region.
D. Bicycling is free but racquetball costs $20 per hour to play. Write the objective function for this scenario. How much time should she spend on each activity in orde to minimize costs?
E. How much time should she spend on each activity if she just wants to maximize her calorie burn?
The diagram has the line 4x+3y=12 dividing the Cartesian Plane into seven regions. Write a system of inequalities the describes region D.
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In this post, wording is  and the problem is posed  .
Indeed, it says " Sharon wants to spend no more than 12 hours exercising a week and wants to burn a  of 7000 calories. "
According to this wording, @Theo in his solution writes and uses inequality
700x + 350y <= 7000.
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To get this " goal ", Sharon should do NOTHING.
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Actually, her wish/goal/target, formulated in the RIGHT WAY, is to burn  7000 calories.
The correct inequality for it is
700x + 350y >= 7000.
opposite to that used by @Theo.
There is no need to explain the feasibility domain is totally different.
Also, regarding the last line in your post, it seems that it mistakenly came from another problem.
In addition, the conception of region D is not defined,
so we actually do not know what these words mean.
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