Question

the sugar - sweet company is going to transport its sugar to market. it will cost $4725 to rent trucks, and it will cost an additional $175 for each ton of sugar transported. let $c$ represent the total cost (in dollars), and let $s$ represent the amount of sugar (in tons) transported. (a) write an equation relating $c$ to $s$. equation: (b) graph your equation using the axes below.

Explanation:

Step1: Identify fixed and variable costs

The fixed - cost of renting trucks is $4725$ and the variable cost is $175$ per ton of sugar.

Step2: Write the cost - function equation

The total cost $C$ is the sum of the fixed cost and the variable cost. The variable cost for $S$ tons of sugar at $175$ per ton is $175S$. So the equation is $C = 175S+4725$.

Answer:

(a) Equation: $C = 175S + 4725$
(b) To graph the equation $C = 175S+4725$, we first identify the $y$ - intercept. When $S = 0$, $C=4725$, so the line crosses the $C$ - axis at the point $(0,4725)$. The slope of the line is $m = 175$. To find another point, we can let $S = 1$. Then $C=175\times1 + 4725=4900$, so we have the point $(1,4900)$. Plot the points $(0,4725)$ and $(1,4900)$ and draw a straight line through them.