MATH 143 005 – Algebra Max-Min Story Problems – 3/2/07 11 A farmer has 1000 feet of fencing on hand.What are the dimensions of the largest-area rectangular plot he can enclose with thisfencing? What is the area of this plot?Answer:2 A farmer has $3645 to spend on fencing a rectangular plot with one side along thehighway. The fencing along the highway side costs $10/foot, while the fencing for theother three sides costs only $5/foot.What are the dimensions of the plot of largest area he can build? Is it square? What is itsarea?Answer: The dimensions: 121.5 feet along the highway, and 182.25 feet perpendicularto the highway. It is not a square plot. Its area: 22, 143.375 ft2.3 The Big-21 Cinema operators have discovered the following approximate demand data fortheir operation: if they charge $5 for a ticket, about 1500 folks will attend the show, butif they charge $7.50 for a ticket, attendance drops to 1200.Determine the ticket price which will maximize the total revenue for a showing. What isthe maximum revenue? What’s the attendance at this revenue-optimizing price?Answer: An $8.75 ticket price will produce an attendence of 1050 for a revenue of$9187.50. This is the largest revenue Big-21 can attain.4 A tour operator charters an airplane with a 200-passenger capacity. If 200 passengersagree to go, the price will be $400 per passenger. For each passenger under 200, the pricewill rise $20 per passenger. How many passengers must go to give the operator the greatestrevenue? In this case what will each passenger pay for the fare. (Hint: let x = the numberof passengers under 200).Answer: 110 passengers go at $2200 per ticket, for a total revenue of $242, 000.5 An orange grower finds that the average yield is 120 bushels per tree when 50 trees areplanted in the grove. For each additional tree planted, the average yield per tree decreasesby 2 bushels. How many trees should be planted to maximize the yield?Answer: 55 treesMATH 143 005 – Algebra Max-Min Story Problems – 3/2/07 26 Here are some data on the monthly demand for hickelsnifters in Ada County:Unit Price Number Sold$7 4$5 12Suppose the sole source for hickelsnifters is a low-overhead factory which costs $6 a monthto keep open. Suppose further that it costs $4.50 to make each hickelsnifter in this factory.What number of hickelsnifters can the factory operators plan to make in order to maximizetheir profit?Answer:Fri Mar 2 09:06:31 MST 2007 /m143.sp07/handouts143/MaxMin302/MaxMin302 from