Hey guys I have a word problem and I was wondering if you could check my work. A factory can product 1,000 bottles per hour. The machine (with setup) cost $3,000,000, whilst each bottle costs .5 cents (labor,materials, etc.) to make. The machine runs 10 hours per day. If each bottle sells for .65 cents, express the cost, revenue and profit for running the factory for X days. After how many days will the factory break even?
Cost function, C(x) = 3,000,000 + .05(10000X)
= 3,000,000 + 5000X
Revenue function, R(x) = .65(10000X)
Profit function, P(x) = 6500X - 3000000 + 5000X
= 11500X - 3000000
Break Even: 3000000 = 11500X
So in approximately 261 days the factory will break even.
Am I right?