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A farmer in California owns 40 acres of land and wants to grow carrots, broccoli, and cauliflower during the winter season. Each crop requires an investment, including purchases of supplies and fertilizer, and manual labor. Growing an acre of carrots requires a $50 investment and 20 hours of manual labor. An acre of broccoli requires a $35 investment and 35 hours of labor. An acre of cauliflower needs a $45 investment and 30 hours of labor. The farmer and her family have $2,500 in their budget and can spend up to 1,000 hours of labor. She expects that the profits from each acre of carrots, broccoli, and cauliflower are $200, $250, and $230, respectively. In order to have a variety of crops for sale, the farmer wants to allocate at least 5 acres for each crop.

A. Formulate a linear programming problem based on the information above and answer the following question: To maximize the total profit, how many acres of land should the farmer allocate to each crop? What is the maximum profit that the farmer can earn? Walk me through the process that you used to answer this question.

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