Question

hw 2.4
score: 1/8 answered: 1/8
question 2
the total cost (in dollars) to produce q units of a good is given by the function:
c(q) = 6.8q + 54000
answer the following. show all of your calculations clearly.
(a) what is the total cost to produce 1700 units?
cost = $
(b) how many units can be produced with a total of $105000?
answer =
question help: video

Explanation:

Part (A)

Step 1: Substitute \( q = 1700 \) into \( C(q) \)

We have the cost function \( C(q)=6.8q + 54000 \). To find the cost for \( q = 1700 \) units, we substitute \( q = 1700 \) into the function. So we get \( C(1700)=6.8\times1700 + 54000 \).

Step 2: Calculate \( 6.8\times1700 \)

First, calculate \( 6.8\times1700 \). \( 6.8\times1700=6.8\times1000+6.8\times700 = 6800+4760=11560 \).

Step 3: Add 54000 to the result

Now, add 54000 to 11560. \( 11560 + 54000=65560 \).

Step 1: Set \( C(q)=105000 \) and solve for \( q \)

We know that \( C(q)=6.8q + 54000 \), and we set \( C(q) = 105000 \). So we have the equation \( 6.8q+54000 = 105000 \).

Step 2: Subtract 54000 from both sides

Subtract 54000 from both sides of the equation: \( 6.8q+54000 - 54000=105000 - 54000 \). This simplifies to \( 6.8q=51000 \).

Step 3: Solve for \( q \)

Now, divide both sides by 6.8 to solve for \( q \). \( q=\frac{51000}{6.8} \). Calculate \( \frac{51000}{6.8}=7500 \).

Answer:

(A):
\( \$65560 \)

Part (B)