Chapter 6.5, Problem 36PPE

a.

To determine

To write: an equality that represents the given situation and graph it.

Answer to Problem 36PPE

  $10x+8y\ge 800$

Explanation of Solution

Given information:

A student earns $10 per hour with two summer jobs at a café and $8 per hour at a market. And the student would like to earn at least $800 per month.

Let the student work $x$ hours per month at the café.

Then his total earning per month at the café is $10x$

Let the student work $y$ hours per month at the market.

Then his total earning per month at the market is $8y$

Total earning of the student is $10x+8y$ per month

Also the student wants to earn at least $800

Then the required inequality is given by, $10x+8y\ge 800$

And its graph is as follows-

  

b.

To determine

To state: whether the student can earn at least $800 per month or not.

Answer to Problem 36PPE

No

Explanation of Solution

Given information:

The student works 60 h per month at the market and can work at most 90 h per month.

Since the student can work at most 90 h and he works 60 h at the market, then he has to spend only 90-60=30 hours at the café.

Then $x=30\text{ and }y=60$

And student can earn at least $800 if the above order pair lies in the shaded region or satisfies the inequality $10x+8y\ge 800$.

The above order pair does not lie in the shaded region then the student cannot earn at least $800 per month.