Optimizations: I need help on problem number 3: Dynamic Programming Problem Mr.

Question

Optimizations:
I need help on problem number 3: Dynamic Programming Problem Mr. Chick N. Little, owner of Shopping Basket Markects, has a wek' supply of eggs to distribute among his stores. Little figures he can maximize profit by simply not putting all eggs in one Shoppus Basket. Below is a table of store. # of crates! Store 1 values of net profit associated with distributing 0 to 3 crates to each Store 2 Store 3 Store 4 0 4 3 10 8 69 14 15 14 13 3 t at w each nife Van EV 13 Store 2. Store 3:o Gtore T Dolors

Explanation / Answer

3) This is the original cost matrix:

Make the matrix square

The cost matrix contains more rows than columns, we add dummy columns with zeros to make the matrix square:

Subtract row minima

Because each row contains a zero, subtracting row minima has no effect.

Subtract column minima

We subtract the column minimum from each column:

Cover all zeros with a minimum number of lines

There are 2 lines required to cover all zeros:

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 0.05. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

Cover all zeros with a minimum number of lines

There are 3 lines required to cover all zeros:

Create additional zeros

The number of lines is smaller than 4. The smallest uncovered number is 0.15. We subtract this number from all uncovered elements and add it to all elements that are covered twice:

Cover all zeros with a minimum number of lines

There are 4 lines required to cover all zeros:

The optimal assignment

Because there are 4 lines required, the zeros cover an optimal assignment:

This corresponds to the following optimal assignment in the original cost matrix:

The schedule is as follows

Assign additional team 1 to site 2,

Additional team 2 to site 1 and

Additional team 3 to site 3

The minimum failure probability = 0.85.

0.60 0.80 0.70 0.40 0.40 0.50 0.25 0.30 0.30 0.20 0.20 0.20

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