Question

If the producer of a commodity spends x thousand dollars on advertising, then Q(x)=43-10e^(-1/2x) thousand units of the commodity will be sold.

(a) How many units will be sold if no money is spent on advertising? How many units will be sold if 5,000 dollars are spent on advertising?

(b) How much should be spent on advertising to sell 40,000 units?

(c) Compute the limit limx→∞ Q(x). What does this limit mean in the given context of the problem?

Please show step by step! Thank you

Answer 1

a)

Given

If no money is spent X=0

33000 units can be sold

If spent $5000 that's 5 thousands then x=5

42179.15 can be sold

Rounding to nearest whole number we get

Q=42179 units

b)

Given

Since Q is in thousands

Q(x) = 40

So

Taking Natural logerithm on both sides we get

X is in thousands

So answer is

x= $2407.95

c)

Q=43000 units

This limit means if we keep spending more on advertisement then definitely we can sell more quantity . But it will reach a saturation and that's 40000 unit which can a producer maximum can sell. After that even if we spend money on advertisement we can't increase quantity ofcof that can be sold