I am having trouble setting up three problems to solve using The Simplex Method

Question

I am having trouble setting up three problems to solve using The Simplex Method for Excel. The equations I am coming up with to input are not working, The political pollster Canter is preparing for a national election. It would like to poll at least 1,500 Democrats and 1,500 Republicans. Each mailing to the East Coast gets responses from 100 Democrats and 50 Republicans. Each mailing to the Midwest gets responses from 100 Democrats and 100 Republicans. And each mailing from the West Coast gets responses from 50 Democrats and 100 Republicans. Mailings to the East Coast cost $40 each to produce and mail, mailings to the Midwest cost $60 each. And mailings to the West Coast cost $50 each. How many mailings should Canter send to each area of the country to get the responses it needs at the least possible cost? What will it cost?

Explanation / Answer

let no of mail send to east coast be "x" , midwest be "y" and west coach be "z".

The equations to be formed are:

100x+100y+50z>1500

50x+100y+100z>1500

x>0,y>0,z>0

40x+60y+50z should be minimum

Using solver in excel we can solve this and I got y=15 as answer, It means she has to send 15 mails to midwest region and it will cost total $900.

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