Help needed setting up an inequalities word problem

Videodrone · #1 $Old$ November 1st, 2009, 09:40 PM

I can't seem to figure out how to set this problem up. I can probably solve it, but I can't get anywhere unless I can set it up. The question is as follows...

Suppose a TV dealer has stores in Annapolis and Rockville, and warehouses in College Park and Baltimore. The cost of shipping sets from College Park to Annapolis is $6 per set; from College Park to Rockville, $3; from Baltimore to Annapolis, $9; and from Baltimore to Rockville, $5. Suppose Annapolis store orders 25 sets and the Rockville store orders 30. Also, suppose that the College Park warehouse has 45 sets in stock, and that the Baltimore warehouse has 40 sets. What is the most economical way to ship the requested TV sets to the two stores, and what is the minimum cost?

Let X1 = the number of sets shipped from College Park to Rockville.
Let X2 = the number of sets shipped from College Park to Annapolis.

I know it's going to be an inequality set with mixed constraints because I have to solve using the Big M method. I appreciate any help that can be given. Thanks in advance

Grandad · #2 $Old$ November 2nd, 2009, 03:47 AM

Hello Videodrone

Welcome to Math Help Forum!

Quote:

Originally Posted by Videodrone $View Post$

I can't seem to figure out how to set this problem up. I can probably solve it, but I can't get anywhere unless I can set it up. The question is as follows...

Suppose a TV dealer has stores in Annapolis and Rockville, and warehouses in College Park and Baltimore. The cost of shipping sets from College Park to Annapolis is $6 per set; from College Park to Rockville, $3; from Baltimore to Annapolis, $9; and from Baltimore to Rockville, $5. Suppose Annapolis store orders 25 sets and the Rockville store orders 30. Also, suppose that the College Park warehouse has 45 sets in stock, and that the Baltimore warehouse has 40 sets. What is the most economical way to ship the requested TV sets to the two stores, and what is the minimum cost?

Let X1 = the number of sets shipped from College Park to Rockville.
Let X2 = the number of sets shipped from College Park to Annapolis.

I know it's going to be an inequality set with mixed constraints because I have to solve using the Big M method. I appreciate any help that can be given. Thanks in advance

You have set this out beautifully. All you need to do now is to write down the various constraints and the total cost. Then minimise the cost.

College Park has $45$ in stock. So

$x_1+x_2\le45$

Baltimore has $40$ in stock. So

$(30-x_1) + (25-x_2)\le40$ (which you can simplify)

And the total cost, $ $C$ , is:

$C = 3x_1+6x_2 + 5(30-x_1)+9(25-x_2)$ (which also can be simplified)

Can you take it from here?

Grandad

Videodrone · #3 $Old$ November 2nd, 2009, 08:40 AM

Awesome. I think I can go from here. If not I will be back! I really appreciate the help.

Videodrone · #4 $Old$ November 2nd, 2009, 05:17 PM

Ok so now I have a new problem. When I simplified for C i got...

$C = -2x_1 - 3x_2 + 375$

What do I do with that 375? Did i simplify it wrong?

Grandad · #5 $Old$ November 3rd, 2009, 12:40 AM

Hello Videodrone

Quote:

Originally Posted by Videodrone $View Post$

Ok so now I have a new problem. When I simplified for C i got...

$C = -2x_1 - 3x_2 + 375$

What do I do with that 375? Did i simplify it wrong?

No, that's correct. You now have to minimise $C$ , given that $C=375-(2x_1+3x_2)$ . So you'll need to maximise $2x_1+3x_2$ .

(Never having used the Big M method, I should do it graphically, but perhaps you have been told to do it in a particular way.)

Grandad