The revenue for selling x units of a product is $R = 30.75 x$ . The cost of producing x units is $C = 10.65 x + 50,000$ . For the producer to obtain a profit, the revenue must be larger than the cost. For what values of x will this product return a profit? Round your answer to the nearest whole unit.
A) $x 1208$
B) $x 2771$
C) $x 2488$
D) $x 1848$
E) $x 2913$

Question

The revenue for selling x units of a product is $R = 30.75 x$ . The cost of producing x units is $C = 10.65 x + 50,000$ . For the producer to obtain a profit, the revenue must be larger than the cost. For what values of x will this product return a profit? Round your answer to the nearest whole unit.
A) $x > 1208$
B) $x > 2771$
C) $x > 2488$
D) $x > 1848$
E) $x > 2913$

Quizplus · Accepted Answer

To find the values of x for which the product will return a profit, we need to solve the inequality $R > C$. Substituting the given expressions for R and C, we get:$$30.75x > 10.65x + 50,000$$Simplifying:$$20.1x > 50,000$$Dividing both sides by 20.1:$$x > 2487.58$$Rounding to the nearest whole unit, we get:$$x > 2488$$

The Revenue for Selling X Units of a Product Is R=30.75xR = 30.75 xR=30.75x

The Revenue for Selling X Units of a Product Is $R = 30.75 x$