# Maxima and Minima

## Smallest Triangular Portion From A Square Lot

**Problem**

A farmer owned a square field measuring exactly 2261 m on each side. 1898 m from one corner and 1009 m from an adjacent corner stands Narra tree. A neighbor offered to purchase a triangular portion of the field stipulating that a fence should be erected in a straight line from one side of the field to an adjacent side so that the Narra tree was part of the fence. The farmer accepted the offer but made sure that the triangular portion was a minimum area. What was the area of the field the neighbor received and how long was the fence? Hint: Use the Cosine Law.

A. A = 972,325 m^{2} and L = 2,236 m |

B. A = 950,160 m^{2} and L = 2,122 m |

C. A = 946,350 m^{2} and L = 2,495 m |

D. A = 939,120 m^{2} and L = 2,018 m |

## 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 |

## 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 |

## 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