Blog #3

Tammy Bah

12 November 2014

Applied Calculus

Blog #3

Part One: I will be inventing my own hypothetical company called Teeebeeeeezz that produces deep conditioning bottles (12 oz) made from natural ingredients such as olive oil, tree oil and honey.

Part Two:  Teeebeeeeezz is a corporation based in Philadelphia, Pennsylvania that produces deep conditioning bottles (12 oz.) for all color and hair types. The target demographics are women from age 5 +, this product is very safe, sustainable, natural and not tested on animals! We sell 12 oz. bottles of deep conditioner made from natural ingredients such as olive oil, tree oil, and honey from the most natural places in the world such as secret areas in the continent of Africa. The start-up cost for getting the cosmetic lab ready to produces units (deep conditioner) is $160,000 and the cost for producing one unit (one bottle of deep conditioner) is $50/unit. Additionally, this company has been running for about 5 years now and it has been booming since the second year.

Fixed costs for the company include the following:

Equipment: $20,000

Supplies: $10,000

Promotion/Advertising: $7,000

Rent of Office Building: $10,000

Product Research (non-animal testing): $20000

Website: $7000

Utilities: $4000

Electricity/ Maintenance: $20,000

Working Capital: $50,000

Insurance: $12,000

Total Fixed Cost: 160,000

Variable Cost: It cost $50 to produce one (12 OZ) bottle of the deep conditioner

Selling price: for one bottle of the effective deep conditioner is $30 per unit.

Cost Function: C(q) = 160,000 + 50q

Revenue Function: R(q)= 30q

Profit Function: revenue (r)- cost (c)= 30q-(160,000 + 50q)= 20q-160,000

Break Even Point value: r(q) = c(q)= 30q-160,000 + 50q; q=8000 and cost is $168,000.

30q=160000+50q

-50q              -50q

-20q=160000

/-20      /-20

q=8000à The break-even point is at 8000.

                                                             

Cost and Revenue Function Graph: See Graph. Interpretationà The attached graph shows the marginal and revenue cost functions as units sold. The break-even point on the graph shows where the cost and the revenue for teeeebeeeez equal each other; equilibrium. In this case, the cost of producing is not exceeding the revenue and the cost of revenue is not exceeding the cost. This means after selling 8000 units, teeeebeeeez will make a profit. After the break-even point, every bottle of deep conditioner sold, teeeebeez will make a profit. The cost function starts at $160,000 and the revenue starts at 0.

Profit Function Interpretation: The profit function for teeeebeeez shows the function of units. The breakeven point occurs at 8000 units sold. When the quantity passes 8000 units teeeebeeez will start to make profit (+ y axis) and when the quantity of below 8000 units, teeeebeeez will have a loss of profit (- y axis). When the line starts to pass the 0 mark, teeebeeezz will be seeing dollaaa signzz #rihanna

Part Three:

Daily basis: n is 200, so q = 200 units

Marginal Cost: $50 for producing the 200^th unit

Average Cost: C(q) = 160,000 + 50(200)/200= $850, the average cost of producing 200 units per day is $850.

1.     The marginal revenue is less than the marginal cost at q=200, this is because in order for there to be a profit. MC>MR. MC=$50, MR= $30. R’(q)=$50, C’(q)=$30 and this is not the case here with the company.

2.     The number of units sold daily (q=200) is before or below the breakeven point of 8000 units. This means that teeebeeez is not making a profit L This is due to all the expensive ways to produce the deep conditioner, it will take many days or even weeks to make a profit.  

3.     R(q+1)-R(q)= 30 ; C(q+1)-C(q)= 50 30<50, so no profit even if production is increased by one extra quantity per day.

4.     When q=200, an increase in production will decrease the average cost

5.     I think that decreasing the average cost will be a lot better for teeeebeeeeez because lower cost will result in increases in profits for each unit sold. $$$$

Part Four:

1.     Based on all of the information, the company will most likely tank in the next five years this is because q is below the break-even point and it will take many days for teeeebeeez to make a profit to sustain the company made for treating hair in a natural way.

2.     Economically, using natural products are a lot more expensive. Teeebeeez will most likely tank in the next five years, unless the economy picks back up and if teeebeeeeez receives a very generous donation. There is no chance for teeebeeeeez as MR>MC, which does not generate a profit. The profits of teeebeeeeez will decline; hopefully the company will not be force to shut down. Teeebeeeeez should try to invest in the company or other assets to regain capital to put into the company and rebuild. I’d also like to add that society should try to be investing in more expensive products such as the deep conditioner because it last longer and it is more beneficial and healthy for them; instead of going for a product that is cheap, yet tested on poor innocent animals and unhealthy.