A commercial bakery allocates 72% of its weekly flour supply to baking bread. After upgrading their supply agreement, the weekly flour supply increases by 13%. Consequently, the amount of flour allocated to bread increases by 2160 kg, while the reserve storage allocation increases by 31%. Determine the bakery's new weekly flour allocation for baking bread.

The correct option is 38160 kg.

To find the new weekly flour allocation for baking bread, we can break down the problem by setting up algebraic equations based on the percentages given.

Step 1: Define the initial allocations
Let the initial total weekly flour supply be $S$ kg.
- Initial flour allocated to baking bread = 72% of $S$ = $0.72\times S$ kg.
- Initial flour allocated to reserve storage = (100% - 72%) of $S$ = 28% of $S$ = $0.28\times S$ kg.

Step 2: Account for the supply increase
The weekly flour supply increases by 13%. Therefore, the total increase in supply is:

$\text{Total Increase in Supply}=0.13\times S$

Step 3: Account for the individual increases in allocations
- Increase in flour for baking bread = 2160 kg.
- Increase in reserve storage allocation = 31% of the initial reserve allocation:

$\text{Increase in Reserve}=0.31\times (0.28\times S)=0.0868\times S$

Step 4: Set up and solve the equation for initial supply
The total increase in flour supply must equal the sum of the increases in bread allocation and reserve storage allocation:

$\text{Total Increase in Supply}=\text{Increase in Bread Allocation}+\text{Increase in Reserve Allocation}$

$0.13\times S=2160+0.0868\times S$

Subtract $0.0868\times S$ from both sides:

$(0.13-0.0868)\times S=2160$

$0.0432\times S=2160$

$S=\frac{2160}{0.0432}=50000\text{kg}$

Step 5: Calculate the new flour allocation for baking bread
Initial flour allocated to bread:

$0.72\times 50000=36000\text{kg}$

Since the allocation for bread increases by 2160 kg, the new weekly allocation for bread is:

$\text{New Bread Allocation}=36000+2160=38160\text{kg}$

Thus, the bakery's new weekly flour allocation for baking bread is 38160 kg.