Suppose that in a given store, customers are willing to buy y pounds of coffee beans...

Suppose that in a given store, customers are willing to buy y pounds of coffee beans per day at $x per pound, as given by the price-demand equation y=10+(180/x) for 2 (is less than or equal to) x (is less than or equal to) 10.

a. Find y’ with appropriate units. Explain what the first derivative means in this situation by hand.

b. Find the demand and the instantaneous rate of change of demand with respect to price when the price is $5.

c. Use a table of values to sketch a well-labelled graph of this function between $2 and $10 per pound.

d. Does the rate of demand increase or decrease over time? Explain.

Solutions

Expert Solution

Differentiate y with respect to x to get y'. Then evaluating it at x=5 to get the instantaneous rate of change in demand with respect to price when the price is $5.

We have evaluated the value of y at x=2,3,...., 10. Then, the graph is to be plotted, as done in the solution.

milcah answered 1 year ago

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