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Total Fixed Costs

Decent Essays

The product my business has chose to produce is water bottles. After some research it can be said that the typical production cost of one water bottle unit is $20. Total fixed costs for my company including rent and utilities are $4000 per month. Given these numbers a linear cost function for my product can be constructed; C(x) = 20x + 4000. In this equation x represents water bottles produced each month at a price of $20 along with $4000 of total fixed costs. An estimated total cost per month can then be determined of $120,000 looking at what the company can afford. Using the cost function C(x), we can plug in 120,000 to then determine the number of water bottles produced each month, which will be x. The beginning equation is C(120000) = 20x + 4000, begin by subtracting 4000 from each side leaving us with 116000 = 20x then divide both sides of the equation by 20 to get a final answer of x = 5800. This is the number of bottles produced each month. Given the price demand …show more content…

To solve the equation, you plug 3000 in for x and get p(price) = 120. Yes, the unit price of $120 may seem high but because production decreased by almost half and we kept revenue the same the increase in unit price was justified. A function for the elasticity of demand would have to follow the equation E(p) = -pf’(p)/f(p). The predetermined function for f(p) = 12000-75p and taking the derivative f’(p) = -75, these can be plugged into the elasticity demand function to get E(p) = 75p/12000-75p. Using the unit price of $120 for p elasticity of demand comes out to be 3. Since 3 is greater than 1 the unit elasticity at this price is elastic. Based on this finding increasing this price would make revenue less productive and so we should keep the price of the water bottles lower to be able to produce more; however, it would make sense to increase

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