midtermIE5112

# C suppose that the florist has the option to purchase

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(c) Suppose that the florist has the option to purchase 10 additional shrubs at a cost of \$5 per shrub. Is this a good idea? Could the florist increase her total profit by doing this?

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set Flower; set Layout; param available {Flower}; param profit {Layout}; param usage {Layout, Flower}; var x {Layout} >= 0; maximize z: sum {i in Layout} profit[i] * x[i]; s.t. inventory {j in Flower}: sum {i in Layout} usage[i,j] * x[i] <= available[j]; data; set Flower := tulip daffodil shrub; set Layout := one two three; param available := tulip 1000 daffodil 800 shrub 100; param profit := one 50 two 30 three 60; param usage : tulip daffodil shrub := one 30 20 4 two 10 40 3 three 20 50 2; Figure 1: AMPL model for problem 6
ampl: model flowers.mod; ampl: option solver cplex; ampl: option cplex_options ’sensitivity’; ampl: solve; CPLEX 11.2.0: sensitivity CPLEX 11.2.0: optimal solution; objective 1512.5 2 dual simplex iterations (1 in phase I) suffix up OUT; suffix down OUT; suffix current OUT; ampl: display x.lb, x, x.ub, x.rc; : x.lb x x.ub x.rc := one 0 21.25 Infinity 0 three 0 7.5 Infinity 0 two 0 0 Infinity -29.375 ; ampl: display inventory; inventory [*] := daffodil 0.875 shrub 8.125 tulip 0 ; ampl: display inventory.down, inventory.current, inventory.up; : inventory.down inventory.current inventory.up := daffodil 500 800 2500 shrub 32 100 130.909 tulip 787.5 1000 1e+20 ; Figure 2: AMPL session for problem 6
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