Use the scenario below to answer all of the questions. Show all of your work on handwritten pages. Take pictures of your page. Upload the pictures to this assessment on Engage. A farmer in upstate New York has a 100-acre farm to plant red beans and romaine lettuce. Every acre planted with beans requires 50 gallons of water per acre and consumes 20 pounds of fertilizer. Every acre planted with lettuce requires 75 gallons of water and 15 pounds of fertilizer. The farmer estimates that is will take 2 hours of labor to harvest each acre planted with beans and 2.5 hours to harvest each acre planted with lettuce. She believes that beans will sell for about $3 a bushel and lettuce at $1 per 3 head bundle. Every acre planted with beans is expected to yield 90 bushels. Every acre planted with lettuce is expected to yield 300 bundles. The farmer can pump 6,000 gallons per day for irrigation. She can buy fertilizer at $10 per 50-pound bag. She can hire laborers at $5 per hour. The farmer can sell all of the beans and lettuce she produces. 1. Let R be the number of acres of red beans planted and Lthe number of acres of lettuce planted. Express the farmer's constraints in terms of these decision variables. What are the units of the right-hand side constraint assumptions? 2. What is the profit per acre of beans and lettuce? Express the objective function in terms of R and L. Is this a minimization or maximization problem? 3. If the farmer produces 50 bushels of beans and 80 bundles of lettuce is the solution feasible, or not, and why? 4. Which constraints are binding if the optimal solution is 60 acres of beans and 40 acres of lettuce and why? What does an allowable increase of 1500 for the water constraint mean? 5. The farmer wants to plant black beans (B) as well on the same plot. Black beans require 45 gallons of water, 25 pounds of fertilizer per acre, and the same labor as red beans. The black beans are expected to sell for $3.25 per bushel and yield 100 bushels per acre. If the shadow price for water is 1.14 and for acreage is 199, should the farmer plant this crop