how many units of product A and B should I make to maximize profit given limited labor and material
Your shop floor makes two products. Jackets earn $40 profit per unit; t-shirts earn $15. Your production lead says "obviously, prioritize jackets." But you only have 40 hours of Labor this week - and a jacket takes five times longer to sew than a shirt. What do you actually tell the floor to build?
Profit is Revenue minus total costs - the line on your P&L that tells you whether you're creating wealth or burning it. The real operator skill isn't computing Profit; it's maximizing it by choosing the right product mix when Labor, materials, and capacity are all finite.
Profit = Revenue - Total Costs. If your shop does $100,000 in Revenue and spends $85,000 to produce and deliver everything, your Profit is $15,000.
You already know the two ingredients. Revenue is the money coming in per unit sold. Cost Per Unit tells you what each unit costs to make. Profit connects them:
Profit per unit = Revenue per unit - Cost Per Unit
Multiply by quantity and you get total Profit. But that formula hides the hard part: which units should you produce, and how many, when your resources are limited? That decision - not the arithmetic - is what operators actually get paid to make.
Revenue is the ceiling. Profit is what you keep.
You can run a $10M Revenue business and lose money every month if your Cost Structure eats it all. Profit is the only line on the P&L that turns into Cash Flow you can reinvest - into Capital Investment, new hires, better equipment, or just surviving a slow quarter.
For an operator with P&L ownership, Profit isn't a report someone hands you. It's the output of every resource allocation decision you make. Every hour of Labor you point at Product A is an hour unavailable for Product B. Every dollar of material cost spent on one SKU is a dollar you can't spend on another. Profit maximization is really an Allocation problem - and the operator who understands that will outperform the one who just watches the scoreboard.
Build up in three layers.
If you only make one thing, Profit math is multiplication:
Total Profit = (Revenue per unit - Cost Per Unit) × Quantity sold
Make as many as you can sell. Done.
Now you make t-shirts and jackets, but you have limited Labor hours. Jacket profit per unit ($40) beats t-shirt profit per unit ($15). Make all jackets?
Not so fast. You need to measure marginal contribution per unit of your Bottleneck resource - the one that runs out first.
| T-shirt | Jacket | |
|---|---|---|
| Profit per unit | $15 | $40 |
| Labor hours per unit | 1 hr | 5 hrs |
| Profit per labor hour | $15/hr | $8/hr |
T-shirts generate nearly twice the Profit per constrained hour, despite lower per-unit Profit. With 40 hours, all-shirts yields $600; all-jackets yields $320. The "less profitable" product wins.
Real production has multiple constraints - Labor and material cost budgets, capacity limits, and more. When two resources bind, pure strategies (all-A or all-B) almost always leave one resource idle. The right answer is usually a mix of products that keeps all scarce resources working.
The key insight: every constraint you add makes the optimal answer harder to eyeball, but the principle never changes - maximize Profit per unit of whatever resource is scarcest.
You're making a Profit decision whenever you:
A small apparel shop makes t-shirts and custom jackets. T-shirts: $25 Revenue, $10 Cost Per Unit, $15 Profit per unit, 1 hour of Labor each. Jackets: $100 Revenue, $60 Cost Per Unit, $40 Profit per unit, 5 hours of Labor each. The shop has 40 hours of available Labor this week. No material constraint yet.
Calculate Profit per unit: T-shirt = $25 - $10 = $15. Jacket = $100 - $60 = $40. Jackets look 2.7x better.
Calculate Profit per Labor hour (the Bottleneck resource): T-shirt = $15 / 1 hr = $15/hr. Jacket = $40 / 5 hrs = $8/hr. T-shirts are 1.9x better on the scarce resource.
All-jacket week: 40 hrs / 5 hrs = 8 jackets × $40 = $320 total Profit.
All-shirt week: 40 hrs / 1 hr = 40 shirts × $15 = $600 total Profit.
Result: The 'less profitable' product generates 87% more total Profit because it uses the Bottleneck resource more efficiently.
Insight: Per-unit Profit is misleading when resources are constrained. Always divide Profit by the Bottleneck resource to find what actually maximizes your P&L.
Same shop, same products. Now add a material constraint: t-shirts need 2 yards of fabric, jackets need 3 yards. The shop has 40 hours of Labor AND 60 yards of fabric this week.
Test all-shirts: 60 yards / 2 yards = 30 shirts max (material binds before Labor). Uses 30 Labor hours, leaving 10 idle. Profit = 30 × $15 = $450.
Test all-jackets: 40 hrs / 5 hrs = 8 jackets (Labor binds first). Uses only 24 of 60 yards. Profit = 8 × $40 = $320.
Notice the waste: all-shirts leaves 10 Labor hours idle; all-jackets leaves 36 yards idle. A mix should do better.
Try 25 shirts + 3 jackets: Labor = 25 + 15 = 40 hrs (exactly at limit). Material = 50 + 9 = 59 yards (just under limit). Profit = $375 + $120 = $495.
Try 20 shirts + 4 jackets: Labor = 20 + 20 = 40 hrs. Material = 40 + 12 = 52 yards. Profit = $300 + $160 = $460. Worse - we shifted too far toward jackets.
The 25/3 mix at $495 beats the best pure strategy ($450) by 10%. Both constraints are nearly fully used.
Insight: When multiple resources constrain production, pure strategies waste capacity on the non-binding constraint. The optimal mix pushes multiple constraints toward their limits simultaneously. That's where maximum Profit lives.
Profit = Revenue - Total Costs is the formula, but the operator's real job is maximizing Profit under constraints - choosing the product mix that squeezes the most value from scarce Labor, materials, and capacity.
Never optimize on Profit per unit alone. Divide by the Bottleneck resource to find the product that generates the most Profit per scarce hour, per scarce dollar, or per scarce machine cycle.
When multiple resources are limited, pure strategies (all-A or all-B) almost always leave some resource idle. The best answer is usually a mix that pushes all constraints toward their limits.
Chasing the highest per-unit Profit without considering resource consumption. A $40-profit jacket that takes 5 hours generates $8/hr; a $15-profit shirt at 1 hour generates $15/hr. The operator who only sees $40 > $15 will leave 47% of potential Profit on the table.
Treating Profit as purely a finance output rather than a production input. Operators who wait for the monthly P&L to learn their Profit are too late - the Allocation decisions that determined that Profit happened weeks ago on the shop floor.
A bakery makes croissants and sourdough loaves. Croissants: $4 Revenue, $1.50 Cost Per Unit, 6 minutes of oven time. Sourdough: $8 Revenue, $3 Cost Per Unit, 30 minutes of oven time. The oven runs 10 hours/day. Which product should the bakery prioritize, and what's the maximum daily Profit if they make only that product?
Hint: Oven time is the Bottleneck. Calculate Profit per minute of oven time for each product.
Croissant Profit = $4 - $1.50 = $2.50/unit. Sourdough Profit = $8 - $3 = $5/unit. Oven time = 600 min/day. Croissant: $2.50 / 6 min = $0.417/min. Sourdough: $5 / 30 min = $0.167/min. Croissants win. Max daily Profit = 600 / 6 = 100 croissants × $2.50 = $250. All-sourdough would yield only 600 / 30 = 20 loaves × $5 = $100.
Same bakery. Now add a constraint: the baker can only shape 80 items per day (croissants and loaves both count as 1 item). Oven is still 600 minutes. Croissants: 6 min oven, $2.50 Profit. Sourdough: 30 min oven, $5 Profit. Find the best integer mix.
Hint: Test the pure strategies first to see which constraint binds. Then try mixes that push both constraints closer to their limits. Check: does shifting one unit from croissants to sourdough help or hurt?
All croissants: oven = 80 × 6 = 480 min (under 600 limit), shaping = 80 (at limit). Profit = 80 × $2.50 = $200. We have 120 min of idle oven. Can we swap some croissants for sourdough to use that oven time? Each swap: lose 1 croissant (free 6 min oven, free 1 shaping slot), gain 1 sourdough (use 30 min oven, use 1 shaping slot). Net: +24 min oven used, +$2.50 Profit per swap. We have 120 spare oven minutes, and each swap costs 24 net oven minutes: 120/24 = 5 swaps. Mix: 75 croissants + 5 sourdough. Oven: 75×6 + 5×30 = 450 + 150 = 600 (at limit). Shaping: 80 (at limit). Profit: $187.50 + $25 = $212.50. That's $12.50 more than all-croissants.
Your production manager says she can hire a part-time worker to add 10 more Labor hours per week at $14/hour. Your current Bottleneck is Labor, and your best product earns $15 in Profit per Labor hour. Should you hire? What's the maximum you'd pay per hour before it stops making sense?
Hint: Each extra Labor hour lets you produce more of your best product. Compare the marginal contribution of that production to the cost of the extra hour. This is the intuition behind Shadow Price - what a scarce resource is worth at the margin.
Each added Labor hour produces $15 of Profit from your best product. Hiring at $14/hr costs $14 to unlock $15 - net gain of $1/hr, or $10/week. Yes, hire. The break-even wage is $15/hr - that's the Shadow Price of your Labor constraint. Above $15/hr, you pay more for the input than the Profit it unlocks. Below $15/hr, every hour purchased is pure marginal contribution to the P&L. Note: this only holds while Labor remains the Bottleneck. If you add enough hours that material becomes the binding constraint, the Shadow Price of Labor drops to zero.
Profit sits directly on top of its two prerequisites. Revenue gives you the top line - money earned per unit sold. Cost Per Unit gives you the bottom-up cost of each unit produced. Profit is what's left when you subtract one from the other, and maximizing it is the core job of any operator with P&L ownership. From here, the concept branches in several directions: break-even asks how many units you need to sell before Profit turns positive at all. Unit Economics zooms in on whether each individual unit contributes positively. Shadow Price formalizes the question from Exercise 3 - what is one more hour of a constrained resource actually worth to your Profit? And EBITDA strips out non-operating items to isolate the Profit your operations actually generated. Every resource allocation decision you make as an operator - where to spend Labor, how to manage material cost, which product to prioritize when capacity is scarce - is ultimately a Profit decision wearing different clothes.
Disclaimer: This content is for educational and informational purposes only and does not constitute financial, investment, tax, or legal advice. It is not a recommendation to buy, sell, or hold any security or financial product. You should consult a qualified financial advisor, tax professional, or attorney before making financial decisions. Past performance is not indicative of future results. The author is not a registered investment advisor, broker-dealer, or financial planner.