Long math problem

[wpatinoxbx8]

Suppose you are selling cases of mixed nuts and roasted
peanuts. You can order no more than a total of 500 cans and
packages and spend no more than $600. How can you maximize
your profit? How much is the maximum profit?
Define:
Let x = number of cases of mixed nuts orderedLet y = number of cases of roasted peanuts ordered
Let P = total profit

Mixed nuts	Roasted peanuts
12 cans per case	20 packages per case
you pay.. $24 per case	You pay...$15 per case
Sell at...$3.50 per can	Sell at...$1.50 per package
$18 profit per case!	$15 profit per case!

	Mixed Nuts	Roasted peanuts	Total
Number of Cases	x	y	x+y
Number of Units	12x	20y	500
Cost	24x	15y	600
Profit	18x	15y	18x+15y

1.Write and simplify the constraints.
2.write the objective (profit) function
3.graph the constraints
4. Find the coordinates of each vertex
5.Evaluate P at each vertex
6.how can you maximize your profit




IM having trouble with the first two because i dont really know what is a constraint.

 

[JeffM]

Suppose you are selling cases of mixed nuts and roasted
peanuts. You can order no more than a total of 500 cans and
packages and spend no more than $600. How can you maximize
your profit? How much is the maximum profit?
Define:
Let x = number of cases of mixed nuts ordered
Let y = number of cases of roasted peanuts ordered
Let P = total profit

1.Write and simplify the constraints.
2.write the objective (profit) function
3.graph the constraints
4. Find the coordinates of each vertex
5.Evaluate P at each vertex
6.how can you maximize your profit

IM having trouble with the first two because i dont really know what is a constraint.

According to the terms of the problem, can you order 600 cans?
According to the terms of the problem, can you spend $800?

Constraints limit what you can do. They are represented by inequalities. In this problem, how many constraints are there? (Hint: there are two implied constraints.) Express each constraint as an inequality using the symbols already assigned to the different variables.

The objective function is what you want to optimize. It is expressed as an equation. So what do you want to optimize? Express that in an equation using the symbols already assigned to the different variables.