1. The property owner wishes to fence the garden plot adjacent to road. Fencing next to road should be sturdier and costs $5 per foot, but other fencing costs just $3per foot. Garden is to have the area of 1200 ft^2.
i) Determine function which models cost of fencing the garden.
ii) Determine garden dimensions which minimize cost of fencing
iii) If owner has at most $600 to s pend on fencing, determine range of lengths he can fence along road.
2. Maximizing area. The wire 10 cm long is cut into 2 pieces, one of length x and other of length 10 - x.
i) Compute the function which models total area enclosed by two squares
ii) Compute value of x which minimizes total area of two squares
3. The Norman window with perimeter 30 ft is to be constructed.
i) Compute the function which models area of window
ii) Compute dimensions of window which admits greatest amount of light.
4. The box with the open top is to made from the rectangular piece of cardboard with dimensions 12 in. by 20 in. by cutting equal squares of both side x at every corner and then folding up sides.
i) Determine function which models volume of box
ii) Determine values of x for which volume is greater than200 in^3.
iii) Determine largest volume that such box can have.