A factory worker makes toys for children. One of the more popular toys are marionette puppets (or 'puppets on strings'). Each puppet requires wooden body parts and cross pieces, clothing and four strings. The worker uses three types of wood - Pine, Cedar and Jarrah. Once the puppets are assembled and sold, they are distributed to toy shops for sale. Puppets are assembled and sold as follows:

Pine Cedar Jarrah

Cost of wooden body parts and cross pieces $15.00 $26.00 $38.00

Cost of clothing $12.50 $15.00 $18.00

Cost of strings (for two) $5.00 $5.00 $5.00

Sale price range $45 - $60 $55 - $70 $75 - $90

Regardless of the type of wood used to make a puppet, there are fixed production costs of $250. Your task is to investigate the cost, revenue and profit associated with each type of truck. Steps to complete the investigation

1. Find the total cost and total revenue functions for each type of puppet and plot these functions on an Excel graph (i.e. you will produce 3 graphs, each with two lines on it). For the revenue function, select a price for each puppet within the price ranges in the table above.

2. Confirm any points of intersection between the cost and revenue function lines using algebra. Express your answer in co-ordinate form.

3. Profit will also differ for each puppet. Find the profit functions and the break-even point for each puppet.

4. Summarise your findings yo ur conclusion: a. Explain the meaning and significance of any points of intersection noted from steps 1 and 2 and any similarities noted from you results in step 3. b. Discuss any differences in profitability between each type of truck (for example, which truck would be easiest to make a profit from?) c. Note any assumptions you have made and any limitations of your findings.