Problem: Singapore company manufactures 50-inch and 75-inch rear projection television sets. Each 50-inch set contributes $225 to profits and each 75-inch set contributes $495 to profits. The company has purchase commitments for 400 50-inch sets for the next month. Although they think they can sell all the 50-inch sets that they could currently make, they do not think they can sell more than 375 75-inch sets. Their factory capacity allows them to make only 975 sets of both sizes total.

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Question: Formulate as a linear programming problem. Please show steps how you get an answer and please be clear in your explanation.