The Challenge
Imagine you have a set of requirements, like staying within a budget (cost constraint) and hitting a specific protein level (nutritional constraint). These constraints form boundaries—think of them as a red line for the maximum cost you can’t exceed and a blue line for the minimum protein level you must meet.
The “Feasible Region”
In the graph below, the shaded region between the red and blue lines is where all the solutions meet both requirements simultaneously. Any solution in this region is valid—it’s below the red line and above the blue line.
However, if you look outside this shaded region:
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To the right of the shaded area: You might be under budget (below the red line) but fail to meet your protein requirement (not above the blue line).
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To the left: You might meet the protein requirement but exceed your budget.
This shaded region represents the space where solutions meet all constraints.
What Happens When You Add Another Constraint?
Let’s say you add a third requirement: sugar = 0 (x = 0). This locks all possible solutions to the y-axis, where sugar is always zero. Now there’s a problem:
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No point on the y-axis satisfies all constraints simultaneously (below the red line and above the blue line).
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This creates an infeasible solution—it’s mathematically impossible to meet all three constraints together.
To fix this, you’d need to remove or adjust one constraint:
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Allow sugar to be non-zero, reopening the shaded region.
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Remove the cost constraint, creating infinite solutions along the y-axis that meet the protein requirement.
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Remove the protein constraint, allowing infinite solutions along the y-axis that stay under budget.
Here it is shown how the feasible area is fixed by losing up both constraints if having sugar = 0 is non-negotiable, albeit highly restricted:
Which Constraint is the Most Restrictive?
In this case, sugar = 0 is the most restrictive—it shrinks the solution space dramatically. But if it’s a non-negotiable requirement (e.g., the product must be sugar-free), the focus shifts to optimizing the narrow space along the y-axis instead of the larger shaded region.
Optimization: Finding the Best Solution
Now, imagine the shaded region as a topo map (a 3D landscape). Each point has a height, representing the best outcome (e.g., taste, cost-efficiency, or nutrition). The goal is to find the highest peak (or lowest valley) that meets all the constraints.
But here’s the challenge: what if the highest peak lies slightly outside the shaded region?
For example:
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If Everest’s summit is just $0.05 outside your cost limit, relaxing the constraint slightly could yield a vastly superior solution.
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On the other hand, if your constraints already include the summit of Pico Cristóbal Colón, there’s no need to explore far outside your boundaries.
This raises a critical question: How do you know if the best solution is just outside your restricted space?
Optimizing for Success
To ensure success when setting constraints, we recommend the following approach:
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Start Broad: Begin without constraints to see if your objectives are feasible. This baseline ensures you aren’t solving an impossible problem.
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Add Non-Negotiables: Introduce must-haves (e.g., sugar-free or regulatory limits) and test feasibility again.
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Introduce Flexible Constraints: Add nice-to-haves. These can be adjusted to balance outcomes.
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Optimize Within the Space: Once you’ve defined the feasible region, optimize for cost, or other important outcomes.
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Test Trade-Offs: Slightly relax constraints and see how it impacts the solution. Is the “Everest” peak worth the extra $0.05 or flexibility in your ingredient levels?
The Key Takeaway
Constraints narrow your options, but they can also blind you to better solutions just outside your reach. The key isn’t just setting rules—it’s iteratively exploring trade-offs and asking:
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What’s negotiable?
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What’s essential?
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What’s the best possible outcome for my product goals?
By approaching constraints methodically, you can find the perfect balance between practicality and innovation.