Question

If the cost to make handmade rubber duckies is modeled by the function ()=4( 1) and the revenue received for rubber duckies is given by ()=11−25 , what is the minimum number of rubber duckies that need to be sold in order for the company to make a profit?

Answer 1

To find the minimum number of rubber duckies that need to be sold in order for the company to make a profit, compare the revenue function with the cost function and solve for x. The minimum number of rubber duckies that need to be sold is 4.

Step-by-step explanation:

To determine the minimum number of rubber duckies that need to be sold in order for the company to make a profit, we need to find the point at which the revenue received is greater than the cost to make the duckies. From the given information, the cost function is C(x) = 4x+1 and the revenue function is R(x) = 11x-25.

Let's set up an inequality to find the break-even point:

R(x) > C(x)

11x-25 > 4x+1

7x > 26

x > 3.71

Since you can't sell a fraction of a rubber ducky, the minimum number of rubber duckies that need to be sold to make a profit is 4.