The annual yield per walnut tree is fairly constant at 50 pounds per tree when the number of trees per 4 acre is 30 or fewer. For each additional tree over 30, the annual yield per tree for all trees on the acre decreases by 1.5 pounds due to overcrowding. a. Express the yield per tree, Y , in pounds, as a function of the number of walnut trees per acre, x. b. Express the total yield for an acre, T, in pounds, as a function of the number of walnut trees per acre, x. c. Find T(10) and T(40). You may use a calculator.
8. The annual yield per walnut tree is fairly constant at 50 pounds per tree when the number of trees per 4
acre is 30 or fewer. For each additional tree over 30, the annual yield per tree for all trees on the acre
decreases by 1.5 pounds due to overcrowding.
a. Express the yield per tree, Y , in pounds, as a function of the number of walnut trees per acre, x.
b. Express the total yield for an acre, T, in pounds, as a function of the number of walnut trees per
acre, x.
c. Find T(10) and T(40). You may use a calculator.
d. Use your knowledge of quadratic functions to determine the optimal amount of walnut trees to be
planted, if one wishes to maximize the the total yield for an acre T. Round to the nearest whole
number.
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