Question: Assume a linear programming (LP) problem. Resource1 has a shadow price of 100 with an allowable increase of 10 and an allowable decrease of 1000.

Assume a linear programming (LP) problem.
Resource1 has a shadow price of 100 with an allowable increase of 10 and an allowable decrease of 1000.
Resource2 has a shadow price of 200 with an allowable increase of 2000 and an allowable decrease of 20.
Resource3 has a shadow price of 0 with an infinite allowable increase and an allowable decrease of 50.
Product1 has a reduced cost of 0.
Product2 has a reduced cost of 0.
Product3 uses 1 of Resource1, 20 of Resource2 and 50 of Resource3, and it has a reduced cost of -1000.
There is an optimal solution in which none of Product3 is produced.
There is no constraint which prevents Product3 from being produced.
Suppose that Product3 can be modified so that it can instead be made with x less of Resource2 and x more of Resource3.
What is the smallest value of x for which there is an optimal solution in which some of Product3 is made?
Give your answer to two decimal places.

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