assume the given product has a linear cost function. use the given information to complete each of the…

assume the given product has a linear cost function. use the given information to complete each of the following. fixed costs are $1600, the cost for 20 items is $2400, and an item sells for $65. (a) find the revenue function. (b) find the cost function. (c) find the break - even point. (d) graph the revenue and cost equations on the same axes. (a) the revenue function is r(x)= . (use integers or decimals for any numbers in the expression.) (b) the cost function is c(x)= . (use integers or decimals for any numbers in the expression.) (c) the break - even point is x = . (d) graph the revenue and cost equations on the same axes. click to enlarge graph

assume the given product has a linear cost function. use the given information to complete each of the following. fixed costs are $1600, the cost for 20 items is $2400, and an item sells for $65. (a) find the revenue function. (b) find the cost function. (c) find the break - even point. (d) graph the revenue and cost equations on the same axes. (a) the revenue function is r(x)= . (use integers or decimals for any numbers in the expression.) (b) the cost function is c(x)= . (use integers or decimals for any numbers in the expression.) (c) the break - even point is x = . (d) graph the revenue and cost equations on the same axes. click to enlarge graph

Answer

Explanation:

Step1: Find revenue function

Revenue is price per item times number of items. Given price per item is $65 and number of items is $x$, so $R(x)=65x$.

Step2: Find variable cost per item

Fixed cost is $1600 and cost for 20 items is $2400. Variable cost for 20 items is $2400 - 1600=800$. Variable cost per item $v=\frac{800}{20}=40$.

Step3: Find cost function

Cost function $C(x)$ is sum of fixed cost and variable - cost. Fixed cost is 1600 and variable cost per item is 40, so $C(x)=1600 + 40x$.

Step4: Find break - even point

Set $R(x)=C(x)$. So $65x=1600 + 40x$. Subtract $40x$ from both sides: $65x-40x=1600$, $25x=1600$. Then $x=\frac{1600}{25}=64$.

Answer:

(a) $R(x)=65x$ (b) $C(x)=1600 + 40x$ (c) $x = 64$ (d) To graph $R(x)=65x$, it is a straight - line passing through the origin $(0,0)$ with a slope of 65. To graph $C(x)=1600 + 40x$, it is a straight - line with a $y$ - intercept of 1600 and a slope of 40. The break - even point is the intersection point of the two lines, which is at $x = 64$. When $x = 64$, $R(64)=C(64)=65\times64=4160$. So the intersection point is $(64,4160)$.