# Maxima and Minima

## Dimensions of the Lot for a Given Cost of Fencing

**Problem**

A rectangular waterfront lot has a perimeter of 1000 feet. To create a sense of privacy, the lot owner decides to fence along three sides excluding the sides that fronts the water. An expensive fencing along the lot’s front length costs Php25 per foot, and an inexpensive fencing along two side widths costs only Php5 per foot. The total cost of the fencing along all three sides comes to Php9500. What is the lot’s dimensions?

A. 300 feet by 100 feet | C. 400 feet by 200 feet |

B. 400 feet by 100 feet | D. 300 feet by 200 feet |

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## Longest Day of the Year: Summer Solstice

**Problem**

The number of hours daylight, *D*(*t*) at a particular time of the year can be approximated by

for *t* days and *t* = 0 corresponding to January 1. The constant *K* determines the total variation in day length and depends on the latitude of the locale. When is the day length the longest, assuming that it is NOT a leap year?

A. December 20 | C. June 20 |

B. June 19 | D. December 19 |

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## 03 Maximum Revenue for Tour Bus of 80 Seats

**Problem**

A tour bus has 80 seats. Experience shows that when a tour costs P28,000, all seats on the bus will be sold. For each additional P1,000 charged, however, 2 fewer seats will be sold. Find the largest possible revenue.

A. P29,000

B. P28,500

C. P28,900

D. P28,700

## Length of one side for maximum area of trapezoid (solution by Calculus)

## 55 - Greatest angle subtended by a picture

**Problem 55**

The lower edge of the picture is a ft, the upper edge is b ft, above the eye of an observer. At what horizontal distance should he stand, if the vertical angle subtended by the picture is to be greatest?