Exam 4: Applications of the Derivative

Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb.The estimated demand for the cookies is 1,000,000 1-lb containers.The setup cost for each production run is $250, and the manufacturing cost is $.30 for each container of cookies.The cost of storing each container of cookies over the year is $.20. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost? Hint: Show that the total production cost is given by the function . Then minimize the function on the interval (0, 1,000,000).

The owner of the Rancho Los Feliz has 2,600 yd of fencing material with which to enclose a rectangular piece of grazing land along the straight portion of a river.If fencing is not required along the river, what are the dimensions of the largest area that he can enclose? What is this area?

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made.If the cardboard is 8 in.long and 3 in.wide, find the dimensions of the box that will yield the maximum volume.

Find the relative maxima and relative minima, if any, of the function.

Select the graph of the function using the curve-sketching guide.

Find the relative maxima and relative minima, if any, of the function.

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle.However, the profit from each bottle beyond 10,000 drops by $0.0002 for each additional bottle sold.Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? Round the answer to two decimal places. The maximum profit is $__________ What would be the price/bottle in this case? Round the answer to the nearest cent. $__________/bottle

Find the horizontal and vertical asymptotes of the graph.

Phillip, the proprietor of a vineyard, estimates that the first 10,000 bottles of wine produced this season will fetch a profit of $2/bottle.However, the profit from each bottle beyond 10,000 drops by $0.0004 for each additional bottle sold. Assuming at least 10,000 bottles of wine are produced and sold, what is the maximum profit? What would be the price/bottle in this case?

Neilsen Cookie Company sells its assorted butter cookies in containers that have a net content of 1 lb.The estimated demand for the cookies is 1,000,000 1-lb containers.The setup cost for each production run is $250, and the manufacturing cost is $.50 for each container of cookies.The cost of storing each container of cookies over the year is $.20. Assuming uniformity of demand throughout the year and instantaneous production, how many containers of cookies should Neilsen produce per production run in order to minimize the production cost? Hint: Show that the total production cost is given by the function . Then minimize the function on the interval (0, 1,000,000). __________ containers of cookies per production run

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing.

Find the relative maxima and relative minima, if any, of the function.Otherwise, answer none. Relative maxima: __________ Relative minima: __________

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 84 in. Find the dimensions of a rectangular package that has a square cross section and the largest volume that may be sent through the mail.Hint: The length plus the girth is (see the figure). Dimensions: _____ x _____ x _____ What is the volume of such a package? __________

Determine where the function is concave downward.

Using the curve-sketching guide, select the graph of the function.

Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. f (x) = -6x + 4

Find the relative extrema, if any, of the function.Use the second derivative test, if applicable.

Find the horizontal and vertical asymptotes of the graph of the function.