Hello Videodrone

Welcome to Math Help Forum! Originally Posted by

**Videodrone** 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 $\displaystyle 45$ in stock. So

$\displaystyle x_1+x_2\le45$

Baltimore has $\displaystyle 40$ in stock. So

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

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

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

Can you take it from here?

Grandad