Profit of a Company P 4000 3500 3000 2500 2000 1500 1000 500 + + + + 10 + 20 30 40 50 60 70 Advertising cost (in thousands of dollars) Profit (in thousands of dollars)

Q: Find the interest earned at 5% compounded continuously for 2 years by a continuous income stream…

A: Given the interest earned r=5%=0.05 , t=2years and PV=1250. We have to find the interest.

Q: 3. A manufacturer determines that when x thousand units of a particular commodity are produced, the…

A: Given that: Profit function: P(x)=-400x2+6800x-12000

Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: Can the average rate of change of an increasing function ever be negative?

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Q: Find the maximum rate of change of f at the point (1, 2). -2/2 2/2 4 -4

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Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

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Q: An asset is purchased for P500,000.00. The salvage value in 25 years is P100,000.00. What is the…

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Q: Find the present value of a continuous stream of income over 3 years if the rate of income is…

A: Given the rate of income , ft=80e-0.08t Number of yearsT=3 Interest rater=11% The present value can…

Q: Suppose that t years from now, one investment plan will be generating profit at the rate of…

A:

Q: What is the x-component of the minimum point of the function in the picture?

A: Given  z=x2+xy+y2-y ∂z∂x=2x+y On putting,  ∂z∂x=0 ⇒2x+y=0 ---> eqn(1) Now, ∂z∂y=x+2y-1 On…

Q: An endowment is to be invested with a continuous interest rate of 3 percent to yield a continuous…

A: From the given information. The continuous interest rate is 3%. The income expression is 1000t. The…

Q: A clothing manufacturer has determined that the cost of producing T-shirts is $0.50 per T-shirt plus…

A: The production cost of t shirts is $0.50 per T shirt. The fixed cost is $315 per month. The selling…

Q: Estimate the average rate of change for the graph above from X=2 to x=3 

A: We have to estimate the average rate of change for the graph above from x=2 to x=3 

Q: The rate of growth of profit (in millions) from an invention is approximated by P'(x) = x e -X,…

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Q: When a wholesaler sold a product at $30 per unit, sales were 186 units per week. After a price…

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Q: (A) Find the exact profit from the sale of the 26th machine. Exact Profit on 26th machine = (B) Use…

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Q: Land bought for speculation is increasing in value according to the formula V – 1000e Ve The…

A:

Q: Air is escaping from a spherical balloon at a rate of 3 cm3/min. At what rate is the surface area…

A: Here given dVdt=3 cm3/min  and r=5cm The volume of the sphere is given by, V=43πr3…

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

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Q: A factory has a monthly operation cost of $280. The graph attached shows the total cost, C, for…

A: As per the question, we will be finding the linear function satisfying the graph. We are given the…

Q: Determine the growth constant of a population that is growing at a rate proportional to its size,…

A: Consider the population size is given as P(t). The expression for the exponential growth rate is…

Q: Find the point of diminishing returns for the revenue function

A: The objective here is to find the point of diminishing returns for the given revenue function:…

Q: Suppose that a product currently sells for $25, with the price increasing at the rate of $2 per…

A: Given, Currently products sells for $ 25  and at this price consumers will buy 150 thousand items.…

Q: Find the present value of a continuous stream of income over 3 years when the rate of income is…

A: Given data- Rate of income   s(t)= $31,000. Time                 = 3 years. The interest rate = 3%.=…

Q: When a wholesaler sold a product at $50 per unit, sales were 208 units per week. After a price…

A: Given that  The demand function is linear. A product is sold at $50 per unit and the sales is 208…

Q: Find the maximum rate of decrease of f at the point (1, 2). None of the above -2/2 2/2 8.

A: To find- Maximum rate of decrease of f at the point(1,2)

Q: Find the present value of a continuous stream of income over 2 years when the rate of income is…

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Q: The demand for a natural resource t years from now will be increasing at a rate of te0.0017 million…

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Q: Find the present value of a continuous stream of income over 4 years when the rate of income is…

A: Given, Rate of income per year is $35000. Interest rate is 4%. Here we shall use the formula for…

Q: A manufacture has been selling 1250 television sets a week at $480 each. A market survey indicates…

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Q: Find the present value of a continuous stream of income over 4 years when the rate of income is…

A: I have appended the formula used in the solution part of the question.

Q: Suppose stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

A: Given: stock A is priced at $30/share and the company will pay a dividend of $0.30/share after two…

Q: Find the marginal revenue function.

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Q: When a wholesaler sold a product at $30 per unit, sales were 280 units per week. After a price…

A: The solution is given below:

Q: The demand function for a company is given by q = Ap) = 3000 – 125p, with p the price in thousands…

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Q: A manufacturer has been selling 1800 television sets a week at $480 each. A market survey indicates…

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Q: The sales of a product produces revenue R(x) where x represents the amount spent on advertising.…

A: Solution :-

Q: Find the marginal profit function.

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Q: 2. As a regular factory worker, a man receives a fixed salary of Php6,000 monthly. He augments his…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: A manufacturer has a monthly fixed cost of $36,000 and a production cost of $7 for each unit…

A: Part a)Formula for profit function:

Q: Use the model to estimate the profit in `1989 y =

A: Given, Y = -0.08 X+ 21.70 where, Y represents profit for a certain company  X represents years after…

Q: Let’s assume that in Kansas, a family farmer sells wheat in a perfectly competitive market. After…

A: Given After increasing the production of wheat from 220 bushels to 240 bushels, the total revenue of…

Q: A retailer Sold 18o units of a product when the price was $30/unit, after a price increase of $5,…

A: We have to fund the cost at which the units to be sold to maximize the revenue.

Q: A tractor is purchased by a local farmer for $ 12,000 and straight - line depreciates to $ 0 in 20…

A: Given that initial price of a tractor is $12,000. Also the value of tractor after 20 years is $0…

Q: Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y…

A:

Q: The price of a share of a company's stock has been decreasing at a constant rate of$0.50 per share…

A: The price of a share of a company's stock has been decreasing at a constant rate of$0.50 per share…

Q: During the Covid-19 pandemic, the number of people that are infected at any time increases at a rate…

A: Solved below

Q: How does time-period or length of run affects the behavior of the supply function?

A: Answer:

Q: Find the present value of a continuous stream of income over 5 years when the rate of income is…

A: On solving this we will get

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.