# LP Problem Formulating

Gotham Motor Oil Company has three warehouses which it can ship products to its three retail outlets. The demand in cans for the product Super Blend is 100 at retail outlet 1; 250 at outlet 2; and 150 at outlet 3. The inventory of this product at warehouse 1 is 50; at warehouse 2 is 275, and at warehouse 3 is 175. The cost of transporting one unit of Super Blend from each warehouse to each retail outlet is shown in the following table. Formulate an LP to determine how many units should be shipped from each warehouse to each retailer so the demand at each retailer is met at a minimum cost.

The way I started solving this is that I made warehouse 1, 2, and 3 become x,y, and z but I didn't know how to get the minimize equation.

I put this:

Minimize (5+8+4)x+(7+9+3)y+(6+10+11)z

and I don't understand what else to do!

Help is very very much appreciated! Thank you!

## 1 Answer

Z=50x+275y+175z where x,y,z are inventory of the product required by ware house 1,2,3, now coming to equation 5x+8y+4z greater than equal to 100,equation 2 7x+9y+3z greater then equal to 250,equation 3-6x+10y+11z greater than 150 then you can make graph and find the value

• Thank you very much – cookiemonster Jul 25 '19 at 3:31