An accountant is identifying the profits for a company. The company's revenues are represented by the function R(x)=30x+155 and the costs by C(x)=13x+2, where x is the number of units sold. Build a profit function.

Question

An accountant is identifying the profits for a company. The company's revenues are represented by the function R(x)=30x+155 and the costs by C(x)=13x+2, where x is the number of units sold. Build a profit function.
(Hint: Profit can be found by subtracting cost from the revenue.)
A. P(x)=17x+153
B. P(x)=17x+157
C. P(x)=43x+153
D. P(x)=−17x−153

GPT-4o mini · Answer

To find the profit function $ P(x) $, we can use the formula: $$ P(x) = R(x) - C(x) $$ Given the revenue function $ R(x) = 30x + 155 $ and the cost function $ C(x) = 13x + 2 $, we can substitute these into the profit equation: 1. Calculate $ P(x) $: $$ P(x) = (30x + 155) - (13x + 2) $$ 2. Distribute the negative sign: $$ P(x) = 30x + 155 - 13x - 2 $$ 3. Combine like terms: $$ P(x) = (30x - 13x) + (155 - 2) $$ $$ P(x) = 17x + 153 $$ Therefore, the profit function is: $$ P(x) = 17x + 153 $$ So, the correct answer is $ A. \ P(x) = 17x + 153 $.