21 QUESTION # 3: SENSITIVITY ANALYSIS 20 POINTS) (CLO 3). The Bradley family owns 410 acres of farmland in North Carolina on which they grow corn and tobacco Each budget of $52,500 for next year. The government limits the number of acres of tobacco that can be planted to acre of corn costs S105 to plant, cultivate, and harvest; each acre of tobacco costs $210. The Bundys have a TOO. The profit from each acre of corn is $300; the profit from each acre of tobacco is S520. The Bradant its graphical and excel solver solution is given as follows: Les 40 "CX-320 * = Number acres of com - 000 - 90 252.000 x3 = Number of acres of tobacco 500 B = 36000 D: 410 X 100 x=0 maximize Z = 300x, +520x, 2 -142.000 Subject to 3001 to know how many acres of each cop to plant to maximize their profit. The linear programming -100 2 142.000 400 Z 123.000 x2 + x3 410 acre) 105x; + 210x2 5 52,500 (Cost) 200 100/4 * S 100 21x220 B Point C is optimal 100 200 300 400 500 600 700 800 0 Reduced Cost Allowable Decrease Objective Coefficient 300 520 0 0 Allowable Increase 220 80 40 220 Variable Cells Final DVS Value X 320 X2 90 Constraints Final Value 91 410 92 52.500 93 90 Shadow Price Orele beets t domad 80 2.095 Constraint R.H. Side 410 52,500 100 Allowable Increase 90 1,050 1E+30 Allowable Decrease 10 9.450 10 0 a) (3 Point) How many acres of farmland will not be cultivated at the optimal solution? Do the Bradleys use the entire 100-acre tobacco allotment? b) (3 Point) What would the profit for com have to be for the Bradleys to plant only corn? (3 Point) If the Bradleys can obtain an additional 100 acres of land, will the number of acres of corn and tobacco they plan to grow change? If yes, clearly state the new values of decision variables and objective function. d) (3 Point) If the Bradleys decide not to cultivate a 50-acre section as part of a crop recovery program, how will it affect their crop plans? e) (4 Point) The Bradleys have an opportunity to lease some extra land from a neighbor. The neighbor is offering the land to them for $110 per acre. Should the Bradleys lease the land at that price? What is the maximum price the Bradleys should pay their neighbor for the land, and how much land should they lease at that price? f) (4 Points) The Bradleys are considering taking out a loan to increase their budget. For each dollar they borrow, how much additional profit would they make? If they borrowed an additional $1,000, would the number of acres of corn and tobacco they plant change? 3