Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible. [Justify your answer.] A rancher has 100 yards of fencing with which to enclose a rectangular corral next to a river. 2. No fencing is required along the river. Find the dimensionstof the corral which will maximize the enclosed fenced area. [Include a figure and use the 2nd Derivative Test to justify your answer.]

Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible. [Justify your answer.] A rancher has 100 yards of fencing with which to enclose a rectangular corral next to a river. 2. No fencing is required along the river. Find the dimensionstof the corral which will maximize the enclosed fenced area. [Include a figure and use the 2nd Derivative Test to justify your answer.]