Abracadabra Inc. purchases three types of products: $1,2,$ and $3$ from two suppliers: A and B$.$ There is a contract cost of $$1,000$ and $$1,500$ associated with each supplier, respectively, if any product is purchased from that supplier. The cost and demand matrix is shown below:

COST $($PER UNIT$)123$ A $$15$ $$10$ $$5$ B $$12$ $$12$ $$6$ SELLING PRICE $$19$ $$17$ $$9$ MAXIMUM DEMAND $900800450$

Formulate a LP problem to maximize profit. $($Hint: Use a binary variable for each supplier with a value of $1$ if that supplier is used and a $0$ otherwise.$)$

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