1. what are the points on x axis and y axis for the isoprofit line through point

Question

1. what are the points on x axis and y axis for the isoprofit line through point (6,6) 2. which best describe the LP? infeasible, unique optimal solution, alternate optimal solution or unbounded ? 3. The formulation of the Organic Greenhouses problem and its graph is shown. Let Pbe the number of acres of peppers planted. Let Tbe the number of acres of tomatoes planted. Max: 30,000P+ 40,000T P+ 17 12 Land 1.5P+3T 30 Labor Ip B T 6 Max Acres of Pepper 0 Non-negativity !34-546-7 s 91011121314 17 18 192021

Explanation / Answer

The slope of profit function -

Writing the line equation in form of y = mx+c

P = Z-40000T/30000

P = Z/30000 -4/3T

The slope of line is -4/3.

The isoprofit line passing through (6,6) and slope -4/3 will be

P = -4/3T+C

Satisfying the equation with (6,6) we get C = 6+4/3x6 =14

The equation of isoprofit line passing through (6,6) will be

P+4/3T =14

All points on x and y axes corresponding to the values of T and P will satisfy this equation.

2. The LP is unique optimal solution type with optimal solution obtained at ( 6,6)

Z= 30000x6+40000x6= 420000

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