Question

the sugar sweet company is going to transport its sugar to market. it will cost $3500 to rent trucks plus $150 for each ton of sugar transported. the total cost, c (in dollars), for transporting n tons is given by the following function.\\( c(n) = 3500 + 150n \\)\
answer the following questions.\
(a) what is the total cost of transporting 11 tons?\
$ \square \
(b) if the total cost is $6950, how many tons is the company transporting?\
\square \text{ tons}

Explanation:

Step1: Solve part (a)

We are given the cost function \( C(n)=3500 + 150n \). To find the total cost of transporting 11 tons, we substitute \( n = 11 \) into the function.
\( C(11)=3500+150\times11 \)
First, calculate \( 150\times11 = 1650 \).
Then, \( C(11)=3500 + 1650=5150 \).

Step2: Solve part (b)

We know that \( C(n)=6950 \) and we need to find \( n \). So we set up the equation:
\( 3500+150n=6950 \)
Subtract 3500 from both sides: \( 150n=6950 - 3500 \)
\( 150n=3450 \)
Divide both sides by 150: \( n=\frac{3450}{150}=23 \).

Answer:

(a) The total cost of transporting 11 tons is \(\$5150\).
(b) The company is transporting 23 tons.