Not sure if I understand your motive correctly...have you decided to accept Kellogg and are hence informing Booth ?
My suggestion is to first wait and see if you receive an admit on the deadline Booth has mentioned and then if you've decided to pursue Kellogg, you can write a polite email to Booth stating the same.
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Oh no. I haven’t decided anything. If I wait 4 weeks for Booth to make a decision, that will pass Kellogg’s acceptance due date. So I was trying to see if Booth can expedite the decision making process.