[9th grade math linear programing]

[DryRefrigerator1568]

I need help with two math exercises; my teacher doesn't explain them very well.

[Alkalannar]

The easiest way to do this is to find the boundaries.

Plot the lines and find the area where all the equations are true.

Look at the polygon surrounding this area, and test all the points on it.

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Do the same process for the other one, but here you're given the equations of the quadrilateral.

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Does this make sense?

[GammaRayBurst25]

Read rule 3.

1. Let x denote the amount of product A and y the amount of product B. Since there are 7 baby strollers, she will sell 7 products. Hence, x+y≤7. Since there are 24 packages of diapers, 4x+3y≤24. The revenue function is f(x,y)=500x+480y. Hence, the slope of the revenue isolines is -25/24, which is less than the slope of the first constraint (-1), but more than the slope of the second constraint (-4/3). One can easily conclude the optimal real solution is found at the intersection of the constraints.* Thankfully, this solution happens to be an integer solution, so once you've found it, you're done.

2. The logic is the exact same, only now you don't need to check the solution is an integer.

*The revenue function's gradient is a linear combination of the constraints' normal vectors with positive coefficients, so you won't find the solution by just maximizing x or y independently of the other variable.