Question

A firm producing lawn chairs has fixed cost of $700.00 per week. The variable cost is $8.00 per chair, and the revenue per chair is $18.00.

A. Write the equation that represent the cost per week, C, for producing x lawn chairs

B. Write the equation that represents the revenue per week, R, from selling x lawn chairs.

C. What is the cost of produxing 100 lawn chairs in a week (show work)

D. What is the revenue from selling 100 lawn chairs in a week. (show work)

E. Using your results from parts c, and d, what is the profit when producing and selling 100 lawn chairs in a week? (hint: Profit =Revenue- Cost (show work)

F. Write the equation that represents the profit in a week, P, from producing and selling x lawn chairs (show work)

hint;: To find the Profit equation take your Revenue equation in part b and subtract your Cost equation in part a)

G Using your Profit equation found in part f.,what is the profit if the company produces and sell 100 lawn chairs in a week (show work)

(substitute 100 in for x in your Profit equation. Note, this should match the answer that you found in part e)

H. How many lawn chair must the company oproduce and sell in a week in order to break even? (hint to find the break even value we can either use R=C or P=0.) (show work)

I What are the Revenue and Cost equal to at this break-even value? (show work)

J. Write the break even point as an ordered pair. (The x-coordinate is the # of lawn chairs and the y-coordinate is the Revenue (or Cost) value.)

K. Below draw the graphs of the cost and revenue equations. Plot and clearly label the break-even point on the graph

Answer 1

Fixed cost of chairs = $700

Variable cost is = $8 per chair

Revenue per chair is = $18

(a) Cost for producing x chairs per week is

(b) Revenue for selling x chairs is

(c) Cost for producing x lawn chair is

So cost for producing x lawn chair is = $1500

(d) As revenue function is:

So revenue for selling 100 chair is

So revenue for producing 100 chair is = $1800

(e) Profit for producing 100 chair is

(f) Profit function is

So profit function is

(g) We have to find P(100)

(f) Break even is when revenue = cost

So we can write

(i) Revenue and cost for x = 70 is