Question

After reviewing the market prices, the investors Frijo-Lane Food Products realized that the prices of the six farms (that they were considering to purchase) have changed to:

Farms Annual fixed costs ($1000)
1 100
2 450
3 150
4 250
5 350
6 300



Therefore, the model version was updated to:

minimize Z = 18x1A +15x1B + 12x1C + 13x2A + 10x2B +17x2C + 16x3A + 14x3B +

18x3C + 19x4A + 15x4B + 16x4C + 17x5A + 19x5B + 12x5C + 14x6A +

16x6B + 12x6C + 100y1 + 450y2 + 150y3 + 250y4 + 350y5 + 300y6

subject to

x1A + x1B + x1C - 11.2y1 <= 0

x2A + x2B + x2C - 10.5y2 <= 0

x3A + x3B + x3C - 12.8y3 <= 0

x4A + x4B + x4C - 9.3y4 <= 0

x5A + x5B +x5C - 10.8y5 <= 0

x6A + x6B + x6C - 9.6y6 <= 0

x1A + x2A + x3A + x4A + x5A + x6A = 12

x1B + x2B + x3B + x4B + x5B + x6B = 10

x1C + x2C + x3C + x4C + x5C + x6C = 14

xij >= 0

yi = 0 or 1

Please indicate which one of the following options IS correct.
a. Farm 3 (y3) should NOT be purchased, according to the model solution.
b. Farm 2 (y2) should NOT be purchased, according to the model solution.
c. Farm 6 (y6) should NOT be purchased, according to the model solution.
d. The Z is exactly the same as the one obtained in the original problem
e. None of the above

Answer 1

The model suggests, based on observed costs, that Farm 3 (y3) should not be purchased due to higher fixed and variable costs, with the model goal being to minimize costs. However, the correct answer would require solving the linear programming problem.

Step-by-step explanation:

Based on the updated model, if we look at the listed fixed costs and the cost coefficients within the objective function, we can infer that Farm 3 (y3) with its annual fixed cost of $150,000 and the associated costs of production (e.g., $16 for x3A, $14 for x3B, $18 for x3C) should NOT be purchased according to the model solution.

This assumption is made with the understanding that the model aims to minimize the total cost, Z, and Farm 3 seems to have a relatively high fixed cost in combination with higher variable costs compared to some other options. However, without solving the complete linear programming model with all constraints, this is a conjecture based on observed values. To determine the absolutely correct answer, the model should be solved using linear programming techniques.