you decide to market your own custom computer software. you must invest $3,255 for computer hardware, and…

you decide to market your own custom computer software. you must invest $3,255 for computer hardware, and spend $2.90 to buy and package each disk. if each program sells for $13.75, how many copies must you sell to break even? a. 196 copies b. 301 copies c. 300 copies d. 195 copies please select the best answer from the choices provided

you decide to market your own custom computer software. you must invest $3,255 for computer hardware, and spend $2.90 to buy and package each disk. if each program sells for $13.75, how many copies must you sell to break even? a. 196 copies b. 301 copies c. 300 copies d. 195 copies please select the best answer from the choices provided

Answer

Explanation:

Step1: Define cost and revenue functions

Let $x$ be the number of copies sold. The total cost $C(x)$ is the sum of the fixed - cost (hardware investment) and the variable cost (cost per disk). So $C(x)=3255 + 2.90x$. The total revenue $R(x)$ is the selling price per copy times the number of copies, so $R(x)=13.75x$.

Step2: Set cost equal to revenue for break - even

At the break - even point, $C(x)=R(x)$. So we set up the equation $3255 + 2.90x=13.75x$.

Step3: Solve the equation for $x$

First, subtract $2.90x$ from both sides: $3255=13.75x - 2.90x$. Then simplify the right - hand side: $3255 = 10.85x$. Now solve for $x$ by dividing both sides by $10.85$: $x=\frac{3255}{10.85}=300$.

Answer:

C. 300 copies