Question 1195573
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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  {{{highlight(highlight(incorrect))}}}  and the problem is posed  {{{highlight(highlight(incorrectly))}}}.


Indeed,  it says  " Sharon wants to spend no more than 12 hours exercising a week and wants to burn a  {{{highlight(maximum)}}}  of  7000  calories. "


According to this wording,  @Theo in his solution writes and uses inequality


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;700x + 350y <= 7000.



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      &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;To get this &nbsp;" goal ", &nbsp;Sharon should do &nbsp;NOTHING.


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Actually, &nbsp;her wish/goal/target, &nbsp;formulated in the &nbsp;RIGHT &nbsp;WAY, &nbsp;is to burn &nbsp;{{{highlight(highlight(at_least))}}} &nbsp;7000 calories.


The correct inequality for it is


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;700x + 350y >= 7000.


opposite to that used by @Theo.



There is no need to explain the feasibility domain is totally different.



Also, &nbsp;regarding the last line in your post, &nbsp;it seems that it mistakenly came from another problem.


In addition, &nbsp;the conception of region &nbsp;D &nbsp;is not defined, 

so we actually do not know what these words mean.