Grade 12 solutions please

CV4U Name: ssignment-Optimization 1. A piece of wire 20 cm long is cut into two pieces. One is bent into the shape of a square and the other into a circle. Where should the wire be cut so that the total area enclosed is a maximum? (5 marks) 2. A rectangle is inscribed (drawn) into a semicircle of radius 3. What are the dimensions of the rectangle with the largest possible area? (5 marks] 3. A rectangular piece of paper is 8.5" wide and 11" high. The lower right hand corner is folded over so as to touch the leftmost edge of the paper. Find the minimum length of the resulting crease (fold line). (5 marks) 4. A rectangular rose garden will be surrounded by a brick wall on three sides and by a fence on the fourth side. The area of the garden will be 1000 m3. The cost of the brick wall is $400/m. The cost of the fencing is $100/m. Find the dimensions of the garden so that the cost of the materials will be minimized. (5 marks) 5. A truck crossing the prairies at a constant speed of 100 km/h gets gas mileage of 8.5 km/litre. Gas costs $2.10 per litre. The truck loses 0.10 km/litre in fuel efficiency for each kilometer per hour increase in speed. The driver is paid $50 per hour in wages and benefits. Fixed costs for running the truck are $20 per hour. If a trip of 450 kilometres is planned, what speed will minimize operating expenses? (5 marks) V4U-Optimization Assignment