# Discussions - Calculus

**Discussion 1**

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Please answer all parts of the following questions (you must show all work):

**1.** Lumyn Electronics is a family owned business. The company sold 128 TV remote controls in July and incurred a total cost of $1,700. In November they sold 248 TV remote controls and incurred a total cost of $3,500. Based on this information, find the following:

a) The marginal cost and monthly fixed cost for this company.

b) A linear function that expresses the company's cost.

c) The revenue and profit (or loss) for this company for the months of July and November, if the average price for each TV remote control sold was $20.

**2.** After starting to turn significant profit, Lumyn Electronics decided that an investment account for their future expansion plans is now necessary. The company's goal is to expand to a major mall location for which $100,000 would be needed. If the investment account pays 12% interest compounded monthly, what would their initial investment have to be in order to reach their $100,000 goal in 5 years?

**Discussion2**

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**1.**

Please research and share two or more different real life applications where differentiation/derivatives apply. You must use reliable sources and cite any source used.

2.

Please answer all parts of the following question (you must use Calculus concepts learned and show all work):

NetSell, a the TV remote control supplier for Lumyn Electronics, has a weekly production cost of q TV remote controls that is given by

C(q) = 0.000004q^{3} - 0.03q^{2} + 100q + 75,000

where q is in the interval [0, 10,000].

The demand function for this product is given by

p(q) = -0.005q + 200.

Based on this information, find the following:

a) The marginal cost for the company.

b) The marginal revenue for the company.

c) The marginal profit for the company when 2,000 and 7,000 TV remote controls are manufactured.

**Discussion3**

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**1.** After an aggressive marketing campaign in the local community, Lumyn Electronics discovered that their cost can now be modeled by the equation: C(n) = 25n^{2} - 1,500n + 25,000, where n represents the number of TV remote controls sold in a particular month.

a) How many TV remote controls must be sold in a month in order to minimize the company's cost?

b) What is that minimum cost?

2.Lumyn Electronics is currently renting their store space from Quality Holdings Corp.

Quality Holdings owns a total of 250 commercial properties available for rent. The company's monthly profit, P, in dollars, is given by the equation

P(n) = -8n^{2} + 3,200n – 80,000

where n is the number of properties rented during a particular month.

a) Would renting out all of the available properties maximize Quality Holdings’ profit?

b) If not, what is the optimum number of properties that the company must have rented in order to maximize its profit?

**Discussion4**

1. Given two functions, f_{1}(x) = 2x and f_{2}(x) = x^{2}, explain what ∫20[f1(x)−f2(x)]ⅆx represents and calculate this integral in the interval [0, 2]. Show all work.

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**2.**

Please answer all parts of the following question (you must use Caclulus concepts learned and show all work):

**1.** Lumyn Electronics has seen stellar expansion in recent months. The company's profit, P, is currently growing exponentially at 5% each year. The rate of change of the company's profit can be modeled as 1PdP=0.05dt. Find a general formula that expresses the profit of the company as a function of time, t.

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