Inequalities Word Problem

A

AutumnSilence

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Nov 10, 2014
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Hello all, I'm a Pre-Calc student and I needed some help solving this one problem. I normally have no issues with Inequalities, but this one has me stumped. I don't even know how to write my constraints. Any help would be appreciated!


A flash drive manufacturer has 370 boxes of a particular drive in warehouse I and 290 boxes of the same drive in warehouse II. A computer store in San Jose orders 350 boxes of the drive, and another store in Memphis orders 300 boxes. The shipping costs per box to these stores is shown below.

WarehouseSan JoseMemphis
I$2.50$2.20
II$2.30$2.10


How many boxes should be shipped to each city from each warehouse to minimize shipping costs? What is the minimum cost?
(Hint: Use x, 350 - x, y, and 300 - y as the variables.)

 
AutumnSilence said:
I normally have no issues with Inequalities, but this one has me stumped. I don't even know how to write my constraints.

A flash drive manufacturer has 370 boxes of a particular drive in warehouse I and 290 boxes of the same drive in warehouse II. A computer store in San Jose orders 350 boxes of the drive, and another store in Memphis orders 300 boxes. The shipping costs per box to these stores is shown below.

WarehouseSan JoseMemphis
I$2.50$2.20
II$2.30$2.10

How many boxes should be shipped to each city from each warehouse to minimize shipping costs? What is the minimum cost?
(Hint: Use x, 350 - x, y, and 300 - y as the variables.)
Click to expand...
For the constraints, a good start would probably be with the variables and expressions they've given you.

You know that 350 need to go to San José, and you need to minimize the cost. You can ship "x" of the units from Warehouse I, and the remaining "350 - x" from Warehouse II. Variable info is similar for the 300 going to Memphis. Then x + y, being the units shipped from Warehouse I, must be less than... what? Similarly, (350 - x) + (300 - y), being the units shipped from Warehouse II, must be less than... what?

The costs for shipping to San José would be 2.5(x) + 2.3(350 - x). What expression would stand for the cost for shipping to Memphis? What do you need to minimize? So what is your optimization equation? And so forth.

If you get stuck, please reply showing your answers to the above questions. Thank you! ;)
 
stapel said:
For the constraints, a good start would probably be with the variables and expressions they've given you.

You know that 350 need to go to San José, and you need to minimize the cost. You can ship "x" of the units from Warehouse I, and the remaining "350 - x" from Warehouse II. Variable info is similar for the 300 going to Memphis. Then x + y, being the units shipped from Warehouse I, must be less than... what? Similarly, (350 - x) + (300 - y), being the units shipped from Warehouse II, must be less than... what?

The costs for shipping to San José would be 2.5(x) + 2.3(350 - x). What expression would stand for the cost for shipping to Memphis? What do you need to minimize? So what is your optimization equation? And so forth.

If you get stuck, please reply showing your answers to the above questions. Thank you! ;)
Click to expand...

So from what I've gathered, would x + y <= 370, and (350 - x) + (300 - y) <= 290.

And then for Memphis the equation would be 2.2(y) + 2.1(300 - y), then?
 
AutumnSilence said:
So from what I've gathered, would x + y <= 370, and (350 - x) + (300 - y) <= 290.

And then for Memphis the equation would be 2.2(y) + 2.1(300 - y), then?
Click to expand...
Then find the expression for the total cost (not just the cost to one of the towns), simplify that expression, add the usual constraints (namely, that the variables cannot be negative), do the graph, find the corner points, etc, etc. In other words, follow the usual process. ;)
 
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