Break-Even Point

Profit Formula

Revenue, total cost, and profit are three exact expressions from the same inputs.

highlighted = computed this step

Revenue line

Revenue is unit price $10 times quantity. Motivation: start with the money coming in.

R(q)=$10qR(q)=\$10q
Break-even pointThe labeled crossing is where revenue equals total cost.break-even point01012$0$100$140revenuetotal costbreak-even q=10quantitydollars

Total cost line

Total cost is fixed cost $60 plus variable cost $4 per unit.

C(q)=$60+$4qC(q)=\$60 + \$4q
Break-even pointThe labeled crossing is where revenue equals total cost.break-even point01012$0$100$140revenuetotal costbreak-even q=10quantitydollars

Profit formula

Profit is revenue minus total cost, so the contribution margin $6 multiplies quantity before fixed cost is subtracted.

Π(q)=$6q−$60\Pi(q)=\$6q - \$60
Break-even pointThe labeled crossing is where revenue equals total cost.break-even point01012$0$100$140revenuetotal costbreak-even q=10quantitydollars

Formula scope

The formula is a model line, not a demand forecast. Break-even analysis assumes the fixed cost, unit price, and unit variable cost are known and stay constant. It does not estimate demand, capacity, taxes, or whether every unit can be sold.

formula from assumed inputs\text{formula from assumed inputs}
Break-even pointThe labeled crossing is where revenue equals total cost.break-even point01012$0$100$140revenuetotal costbreak-even q=10quantitydollars