November 2019

Problem
A contractor can buy a dump trucks for P800,000 each (surplus) or rent them for P1,189 per truck per day. The truck has salvage value of P100,000 at the end of its useful life of 5 years. Annual cost of maintenance is P20,000. If money is worth 14% per annum, determine the number of days per year that a truck must be used to warrant the purchase of the truck.

Problem
Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side x from each corner of the sheet and folding up the sides. Find the value of x that maximizes the volume of the box.

Problem
A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects 2 cell phones at random without replacement. What is the probability that exactly 1 is defective?

Problem
A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

Problem
Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

Problem
A Toyota Land Cruiser drives east from point A at 30 kph. Another car, Ford Expedition, starting from B at the same time, drives S30°W toward A at 60 kph. B is 30 km from A. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.