Question

A farmer wishes to fence in a rectangular field of area 1250 square metres. Let the length of each of the two sides (facing north-south) of the field be z metres, and the length of each of the other two sides (facing east-west) be y metres. The price of normal fencing is S5 per metre. However the northern edge of the fence needs special wind protection, and that will make that edge of the fence three times as expensive, per metre, as the rest of the fence. Use calculus to find the dimensions of the field that will minimise the total cost. Show some justification that your critical point is actually a minimum.
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