Sanjay's Summer Job

Since tutoring pays more, it is obvious that you have to do more tutoring to earn more.

There is a calculus approach but this is the simplest way

25,5 because tutoring pays more than delivering indian food, Therefor, the greater time he spend with tutorial, the greater income he will gain.

12x +8y =max.

spend more time on the tutoring,which pays more than delivering food,which pays less.hence the answer is 25 and 5

25 12=300 $ + 5 8$=40 total is 340 $ it is the highest incme

Income=12x+8y , x=no. of hours of tuition, y=no. of hours of delivery. Hence, by inequality, maximum income=340. Then, x=25 and y=5.

Sanjay gets more money for tutoring than for delivering Indian food. So, he should spend the least number of hours possible in delivering Indian food, that is 5 hours. Rest 25 hours he can tutor.

Let's get a more rigorous solution posted for this LP. Let $x$ be the tutoring hours and $y$ be the delivery hours. We're given that Sanjay wishes to spend between 5 and 20 hours for food delivery (i.e. $5 \le y \le 20$ ), and he wishes to work both jobs up to 30 hours max (i.e. $x \ge 0; x+y \le 30$ ). We can model this according to:

MAX

$\$12 \cdot x + \$8 \cdot y$

Subject to:

$5 \le y \le 20;$

$x+y \le 30;$

$x \ge 0.$

Plotting this system in the $xy-$ plane yields the feasible region:

with the criticial vertices $(x,y) = (0,5); (0,20); (10,20); (25,5)$ . Plugging each of these points into the income objective function gives a maximum amount of $\$340$ , which is attained at the point $\boxed{(x,y) = (25,5)}.$

There are just so many hour combinations. To go through it faster just look at the solutions and find a pair that has the highest ratio for tutoring compared to delivery since it pays more.

tutoring more will fetch more money

Delivary @ Time spend= MIN 5 hr, Income= 5 8= $40; if MAX=20 hr then, Income=20 8=$160. Tution @ Time spend= 25 hr, Income=25 12=$300; if Time=10 hr then, Income=10 12=$120 ============= ================ $340 $180 Max Income= (25,5)

Close your eyes, choice one suggest. That's the best way.

When he tutors, he gets payed more, so he should do food delivery the least and tutoring the most he can.

just trial and error solution on available choices...

Common sense people

25,5 Just imagine....... It's best.

25, 5 of course .. To earn more i should go with my time to the higher income.. Which is tutoring..

25 multiply 12=300 5 multiply 8=40 so he will earn more by doing this

obvious answer, but if need mathematics explain, here: let x number of hours for delivering, 5<=x<20, so (30-x) for tutoring. let A income in a week, we have: 8x + 12(30-x) = A 360 - 4x = A For A the greatest, x must be the smallest, x = 5.

Sanjay can earn more in math tutoring. since it is obvious that he gets more money in tutoring than delivering.

(25,5) combination will maximize his income because tutoring pays more. Therefore, we will allocate more hours in tutoring and less hours in delivering.

Plus Sanjay fait d'heures de tutoring, plus il gagne d'argent . Donc, le meilleur ratio est 25,5.

it is easy term that he not delivery more than 20 hours and least 5 hours , so always he will do less as much as delivery as possible and the 25 and 5 is the most powerful answer for making large money.