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a company runs food service concessions for sporting events throughout the country. their marketing research department chose a particular football stadium to test market a new jumbo hot dog. it was found that the demand for the new hot dog is given approximately by

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KhiradAfaq

Revenue is the cash generated from ordinary enterprise operations, calculated because the common income fee instances the range of gadgets sold.

The required details for Revenue in given paragraph

P = 7 - ln(x) while 5 < x>

Total variety of puppies sold = x thousand

So, overall revenue = x * p

R = x(7 - ln(x))

R = 7x - xln(x)

Company will pay 1 greenback consistent with canine

So, overall cost , C = 1 * x = x

Profit = R - C

P = 7x - xln(x) - x

P = 6x - xln(x)

Deriving :

dP/dx = 6 - d/dx(xln(x))

dP/dx = 6 - x*d/dx(ln(x)) - ln(x)*d/dx(x)

dP/dx = 6 - x(1/x) - ln(x)

dP/dx = 5 - ln(x)

Since this need to be maximized, dP/dx = 0

5 - ln(x) = 0

ln(x) = 5

x = e^5

Now, p = 7 - ln(x)

Plug withinside the cost of x :

p = 7 - ln(e^5)

p = 7 - 5

p = 2

So, every canine need to be priced at $2 to maximize profit

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