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Figure 1. Production, Revenue and Costs for Firm Units Sold Total Revenue Total Cost Revenue Change Cost Change Profit N 2 -- 0 2.5 2 0.5 1.5 3.5 6 10 10 12 20Figure of a production possibilities frontier between two outputs with three points marked. Output 2 B Production Possibilities Frontier A C Output 1Figure 5. Simplex final tableau for two variable crop problem Final Tableau B 51 53 P RHS land 1 -0.0075 -0.00625 50 cash 0 0.0125 -0.00625 130 stor O 0 -0.005 0.0125 0 140 obj 0 0 0.825 0.1875 1 20100 Let C = one acre of corn made and sold; B = one acre of soybeans made and sold $1 = land slack, $2 = cash slack, $3 = storage slack P = objective variableFigure 2 Profit maximizing problem Let- Q is qua-ninthr P is price C is cost H; is revenue Z is prot Q = a + by 'Deinand equation (a 'e U; h t: 0} = d + Q {lost equation (d :r U: o 3:- H} R = P x Q 'Revenue equation 3 = R 0 'Profit equation We can substitute this problem so that we have a function Z for prots that depends only; on price. This equation is: s = we + [a _ egg [d + e*a] We can differentiate this with respect to zero and set it equal to zero to solve for the best price. This derivative equation that solves for price is: agar 2 2m + a {as} = o Table 1. Sensitivity Report from maximizing profits via production of X1 and X2 subject to three constraints (C1, C2 & C3). 6 Variable Cells 7 Final Reduced Objective Allowable Allowable 8 Cell Name Value Cost Coefficient Increase Decrease 9 $B$2 Activity Levels X1 3 0 4 16 4 10 $C$2 Activity Levels X2 5 O 4 1E+30 3.2 11 12 Constraints 13 Final Shadow Constraint Allowable Allowable 14 Cell Name Value Price R.H. Side Increase Decrease 15 SD$6 C1 LHS 13 0 20 1E+30 7 16 $D$7 C2 LHS 20 0.8 20 35 15 17 SD$8 C3 LHS 5 3.2 5 3.888888889 5 an