n this assignment, we revisit the WUWU Problem, which was previously discussed in this week's Lesson $2($specifically in Video $3).$ If you have not done so already, please download the WUWU spreadsheet: it is available for Excel and for LibreOffice.

For the questions below, we will use as our starting point the WUWU $1$ problem, which is found in the WUWU$1$ tab of the spreadsheet $($not the WUWU$2$ tab$).$ As it stands now, the objective function for WUWU$1$ problem has an optimal value of $$6,525\mathrm{.}00.$ Try solving for the problem in its current form: you should get the same value.

The questions below will ask you to modify the parameters of this model, and the model itself, to include new constraints and products.

Part $1$

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For the first variation of the problem, we will change the capacity in both our DCs$.$ Please increase the capacity of the Atlanta DC from $200$ widgets to $300$ widgets, and decrease the capacity of the Boston DC from $500$ widgets to $400$ widgets. Solve optimally.

What is the new minimum cost of the optimal solution?

Please provide your answer in dollars, but using only numbers. For example, for a solution of $$1,234$ you would enter $1234$ as your answer. Do this for all answers to questions about cost in this assignment. Please round your answer to the nearest integer.

$6250$

correct

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Part $2$

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For the second variation, we will build upon Part $1$ and add a new constraint to the problem: the Miami plant will now have an overall capacity constraint of $250$ widgets of any type. Calculate the new minimum cost solution. Compare this new cost to the one in Part $1.$

Did the new constraint that we just added to the problem make any difference in the solution?

No

correct

We invite you to think about why this is so$.$

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Part $3$

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For the third variation, we will build upon Part $2$ and add a new constraint to the problem: the Chicago plant will now have an overall capacity constraint of $250$ widgets of any type. Solve optimally.

What is the new minimum cost of the optimal solution?

Remember to give your answer to this and all cost questions in terms of dollars, using only numbers, and rounding your answers to the nearest integer.

$6400$

correct

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Part $4$

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The fourth variation builds upon Part $3$ and adds two new constraints. First, we add a $150$ widget capacity constraint at the Atlanta DC specific to widget $1.$ In other words, the Atlanta DC can process at most $150$ units of widget $1.$ Second, we add a similar constraint for the the Boston DC specific to widget $2$: the Boston DC can now handle at most $200$ units of widget $2.$

What is the new mi