MATHEMATICS COLLEGE

A garden shop determines the demand function q = D(x) = 5x + 200 / 30x + 11 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant.(a) Find the elasticity.
(b) Find the elasticity when x = 2.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?

Answers

Answer 1

Answer:

Answer: a) $E(x)=(-5945)/((30x+11)(5x+200))$ , b) 0.7975, demand is inelastic, c) increase.

Step-by-step explanation:

Since we have given that

$D(x)=(5x+200)/(30+11)$

So, derivative w.r.t x would be

$D'(x)=(5(30x+11)-30(5x+200))/((30x+11)^2)\n\nD'(x)=(150x+55-150x-6000)/((30x+11)^2)\n\nD'(x)=(5945)/((30x+11)^2)$

As we know that

$E(x)=(-xD'(x))/(D(x))\n\n\nE(x)=((-(-)5945x)/((30x+11)^2))/((5x+200)/(30x+11))\n\n\nE(x)=(5945x)/((30x+11)(5x+200))$

(b) Find the elasticity when x = 2.

So, we put x = 2, we get that

$E(2)=(5945* 2)/((30(2)+11)((5(2)+200)))\n\nE(2)=(11890)/((60+11)(10+200))\n\nE(2)=(11890)/(71* 210)\n\nE(2)=(11890)/(14910)\n\nE(2)=0.7975$

Since, 0.7975 < 1, so the demand is inelastic.

The total revenue will also increase with increase in price.

As total revenue = $price* quantity$

Hence, a) $E(x)=(-5945)/((30x+11)(5x+200))$ , b) 0.7975, demand is inelastic, c) increase.

Answer 2

Answer:

Final answer:

This problem involves the calculation of the elasticity of a demand function using the derivative of the function. The elasticity is then used to analyze the effect on the total revenue when the price changes. The elasticity at a specific point is calculated and used for further analysis.

Explanation:

For part (a), to find the elasticity of the demand function, we need to use the formula for the price elasticity of demand, which is E = (dQ/dX) * (X/Q). Here, dQ/dX is the derivative of the demand function concerning X. This needs to be calculated first. The value of E provides us with the measure of elasticity.

For part (b), when x = 2 we substitute this value into the formula for E to get the elasticity at x = 2.

For part (c), based on the concept of elasticity, if E > 1, the demand is said to be elastic and a price decrease will result in an increase in total revenue, and vice versa. If E < 1, the demand is said to be inelastic and a price decrease will result in a decrease in total revenue, and vice versa. So, after calculating E at x = 2, we can use it to determine the effect on total revenue.

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Answers

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If the principal is $350 and the interest rate is 3 percent, what is the simple interest earned in one year?simple interest = Pxrxt

Answers

Answer:

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Step-by-step explanation:

Given that

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time t= 1 year

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Simply put the extra money earned after an investment is called the simple interest

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Answers

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