Question

Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot work more than 32 hours in a week, but he wishes to earn at least $251 each week. Which work schedule is within Michael’s constraints? 8 hours at the movie theater and 25 hours at the bakery 15 hours at the movie theater and 20 hours at the bakery 19 hours at the movie theater and 12 hours at the bakery 21 hours at the movie theater and 8 hours at the bakery

Answer 1

Answer:

Step-by-step explanation:

Given  

Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot work more than 32 hours ................

Let the number of hours working to the movie theatre be a and number of hours working at the bakery be b

So inequality will be  

a + b < or = 32 hours

9 a + 7 b > or = $ 251

1. Now at the movie theatre is 8 hours and 25 hours at the bakery. So a = 8 and b = 25.

8 + 25 < or = 32

33 < or = 32 hours is not true

2. Now 15 hours at the movie theatre and 20 hours at the bakery. So a = 15 and b = 20.

15 + 20 < or = 32

35 < or = 32 is not true

3.Now 19 hours at the movie theatre and 12 hours at the bakery. So a = 19 and b = 12.

19 + 12 < or = 32

31 < or = 32 is true

Now also 9 x 19 + 7 x 12 > or = $ 251

           $ 255 > or = $ 251 is true

4. Now 21 hours at the movie theater and 8 hours at the bakery. So a = 21 and b = 8.

21 + 8 < or = 32 hours

 29 < or = 32 hours is true

But  

9 x 21 + 7 x 8 > or = $ 251

$ 245 > or = $ 251 is not true.

Therefore the work schedule in the third case is within Michael’s limitations.

Answer 2

Answer:

 19 hours at the movie theater and 12 hours at the bakerywork schedule is within Michael’s constraints

Step-by-step explanation:

Let x be the number of hours he works at theater.

Michael cannot work more than 32 hours in a week

So, equation becomes : $x+y\leq 32$

Let y be the number of hours he works at bakery.

Michael is paid $9 per hour to work at the movie theater.

He earns for working x hours in theater= 9x

He earns $7 per hour when he helps his aunt at her bakery

He earns for working y hours in bakery =7y

Now we are given that  he wishes to earn at least $251 each week.

So, equation becomes : $9x+7y\geq 251$

Now plot the equations on graph

we plot the given constraints

Refer the attached graph , we can see that only ( 19,12) lies in the feasible region.

Hence  19 hours at the movie theater and 12 hours at the bakerywork schedule is within Michael’s constraints