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Answer :
Sure! Let's go through the questions step-by-step.
### (a) What is the total cost of transporting 12 tons?
To find the total cost of transporting 12 tons of sugar, we use the cost function provided:
[tex]\[ C(n) = 5500 + 125n \][/tex]
Here, [tex]\( n \)[/tex] is the number of tons. We need to substitute [tex]\( n = 12 \)[/tex] into the equation.
[tex]\[ C(12) = 5500 + 125 \times 12 \][/tex]
Calculate [tex]\( 125 \times 12 \)[/tex]:
[tex]\[ 125 \times 12 = 1500 \][/tex]
Now, add this to the fixed cost of \[tex]$5500:
\[ C(12) = 5500 + 1500 = 7000 \]
So, the total cost of transporting 12 tons is \$[/tex]7000.
### (b) If the total cost is \[tex]$8125, how many tons is the company transporting?
Here, we have the total cost given as \$[/tex]8125, and we need to find the number of tons, [tex]\( n \)[/tex].
Start with the cost equation:
[tex]\[ C(n) = 5500 + 125n = 8125 \][/tex]
First, subtract \$5500 from both sides to solve for the term with [tex]\( n \)[/tex]:
[tex]\[ 125n = 8125 - 5500 \][/tex]
Calculate the right side:
[tex]\[ 8125 - 5500 = 2625 \][/tex]
Now, divide by 125 to find the number of tons:
[tex]\[ n = \frac{2625}{125} \][/tex]
Calculate the division:
[tex]\[ n = 21 \][/tex]
So, the company is transporting 21 tons.
These are the solutions to the given questions.
### (a) What is the total cost of transporting 12 tons?
To find the total cost of transporting 12 tons of sugar, we use the cost function provided:
[tex]\[ C(n) = 5500 + 125n \][/tex]
Here, [tex]\( n \)[/tex] is the number of tons. We need to substitute [tex]\( n = 12 \)[/tex] into the equation.
[tex]\[ C(12) = 5500 + 125 \times 12 \][/tex]
Calculate [tex]\( 125 \times 12 \)[/tex]:
[tex]\[ 125 \times 12 = 1500 \][/tex]
Now, add this to the fixed cost of \[tex]$5500:
\[ C(12) = 5500 + 1500 = 7000 \]
So, the total cost of transporting 12 tons is \$[/tex]7000.
### (b) If the total cost is \[tex]$8125, how many tons is the company transporting?
Here, we have the total cost given as \$[/tex]8125, and we need to find the number of tons, [tex]\( n \)[/tex].
Start with the cost equation:
[tex]\[ C(n) = 5500 + 125n = 8125 \][/tex]
First, subtract \$5500 from both sides to solve for the term with [tex]\( n \)[/tex]:
[tex]\[ 125n = 8125 - 5500 \][/tex]
Calculate the right side:
[tex]\[ 8125 - 5500 = 2625 \][/tex]
Now, divide by 125 to find the number of tons:
[tex]\[ n = \frac{2625}{125} \][/tex]
Calculate the division:
[tex]\[ n = 21 \][/tex]
So, the company is transporting 21 tons.
These are the solutions to the given questions.
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