Question

4. You are constructing a rectangular storage shed with a square base. You need space to accomodate 75 m of stuff. The floor is made of concrete which costs 2$/m². The four walls are made of wood, which costs 5 $/m². The roof tiles cost 4 $/m2 (a) Write a formula for the total cost of the shed in terms of a single variable. Indicate what this variable represents, and state its domain. (3 marks) (b) What should be the dimensions of the shed to minimize the cost? State the length, width and height, and also the minimum value of the cost. (5 marks) (c) Suppose you only have enough concrete to cover an area of 16 m². How does this change the domain of the variable you chose in part (a)? (1 mark) (d) With the restriction from part (c), can you achieve the minimum cost you