A diet problem includes five foods (pizza, chicken sub, hamburger, Greek salad, & minestrone soup). The diet planner wants to consider calories (must be between 1,500 and 2,000 per day), vitamin A (at least 20 units), & sodium (no more than 14,000 units).

The formulation is as follows (the terms in red indicate parameters that are a function of i):

Min = 4x1 + 6x2 + 3x3 + 2x4 + 7x5

12x1 + 20x2 + 11x3 + 6x4 + 25x5 >= 1500

12x1 + 20x2 + 11x3 + 6x4 + 25x5 2000

2x1 + 4x2 + 4x3 + x4 + 5x5 >= 20

123x1 + 159x2 + 266x3 + 61x4 + 294x5 14800 Solve the problem with LINDO/LINGO

(a) How many servings of each type of food should the planner eat & how much does the diet cost? (b) How many calories, vitamin A & sodium does the diet include? (c) What would happen, if the price of pizza were to drop from $4 to $3.45 per serving? (d) What would happen if the price of chicken sub would drop by $1?

(e) What would happen, if (for i = 0, 1, 2, 3): the upper bound on the calories were to drop to 1,800?

(for i = 4, 5, 6): the lower bound on the calories were to increase to 1,600?

(for i = 7, 8, 9): there would be an upper bound of 328 on vitamin A ?

Licensee info: Eval Use Only License expires: 22 JUL 2022 Global optimal solution found. Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: 434.9081 0.000000 4 0.10 Model Class: LP Total variables: Nonlinear variables: Integer variables: 5 0 0 Total constraints: Nonlinear constraints: 5 0 Total nonzeros: Nonlinear nonzeros: 24 0 Variable X1 X2 X3 X4 X5 Value 0.000000 37.27034 0.000000 0.000000 30.18373 Reduced Cost 8.544882 0.000000 0.6372703 0.2698163 0.000000 Row 1 2 3 4 NMtun Slack or Surplus 434.9081 0.000000 500.0000 280.0000 0.000000 Dual Price -1.000000 -0.3417323 0.000000 0.000000 0.5249344E-02