Question

The cost to produce X units of wire is C =30x +500 while the revenue is R =40x. find all intervals where the product will at least break even.I need help with solving this please

Answer 1

we have that

the cost function is

C =30x +500

the revenue function is

T=40x

Remember that

The profit function is equal to the revenue minus the cost

so

P=R-C

P=40x-(30x+500)

P=10x-500

Break-even is when the profit is zero

therefore

P=0

substitute

0=10x-500

10x=500

x=50

therefore

The product is at least break even

For x ≥ 50 units

the number of units must be greater than or equal to 50

the interval is [50, infinite)