1.5 score: 10/13 answered: 10/13 question 11 to manufacture boxes, it costs $550 (the fixed cost) plus $3…

1.5 score: 10/13 answered: 10/13 question 11 to manufacture boxes, it costs $550 (the fixed cost) plus $3 for each box produced. the boxes are then sold for $5 each. a. find an expression for the production cost of q boxes. b. find an expression for the revenue earned by selling q boxes. c. for what values of q will the revenue be greater than the production cost? (answer in interval notation.) question help: video ebook written example

1.5 score: 10/13 answered: 10/13 question 11 to manufacture boxes, it costs $550 (the fixed cost) plus $3 for each box produced. the boxes are then sold for $5 each. a. find an expression for the production cost of q boxes. b. find an expression for the revenue earned by selling q boxes. c. for what values of q will the revenue be greater than the production cost? (answer in interval notation.) question help: video ebook written example

Answer

Explanation:

Step1: Find production - cost expression

The fixed cost is $550 and the variable cost is $3 per box. So the production cost $C(q)$ of $q$ boxes is the sum of the fixed cost and the variable cost. The variable cost for $q$ boxes at $3 per box is $3q$. So $C(q)=550 + 3q$.

Step2: Find revenue - expression

The boxes are sold for $5 each. So the revenue $R(q)$ from selling $q$ boxes is the price per box times the number of boxes. So $R(q)=5q$.

Step3: Solve for when revenue is greater than cost

We want to find when $R(q)>C(q)$. Substitute the expressions for $R(q)$ and $C(q)$: [ \begin{align*} 5q&>550 + 3q\ 5q-3q&>550\ 2q&>550\ q&>275 \end{align*} ] In interval notation, the solution is $(275,\infty)$.

Answer:

a. $C(q)=550 + 3q$ b. $R(q)=5q$ c. $(275,\infty)$