A factory worker makes teddy bears. Each teddy bear requires two (2) eyes, internal ‘stuffing’, an external body covering and four (4) paw pads. The worker uses three types of body covering – calico, corduroy and velvet. Once the teddy bears are assembled, they are distributed to toy shops for sale. Teddy bears are assembled and sold as follows; Cost of body covering Cost of eyes (individually) Cost of internal ‘stuffing’ Cost of paw pads (per pair) Sale price range
Calico $11.50 $2.50 $6.00 $1.85 $30 - $36
Corduroy $18.50 $2.65 $6.00 $2.90 $40 - $48
V elvet $24.50 $2.75 $6.00 $3.60 $45 - $55
Regardless of the materials used to make each teddy bear, there are fixed production costs of $180. Your task is to investigate the cost, revenue and profit associated with each type of teddy bear.

1. Find the total cost and total revenue functions for each type of teddy bear 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 teddy bear type within the price ranges in the table above.

2. Confirm the points of intersection between the cost and revenue function lines using algebra. Express your final results in co-ordinate point form: (Quantity value, Revenue value)

3. Profit will also differ for each type of teddy bear. Find the profit functions and the break-even quantity for each type.

4. Summarise your findings in 200 words. In your 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 teddy bear (for example, which teddy bear would be easiest to make a profit from?)
c. Note any assumptions you have made and any limitations of your findings.