We have $1080 at our disposal which we will use to buy x units of item 1 and y units of item
2. The benefit or pleasure of buying x units of item 1 and y units of item 2 are given by
U = x × y2
a) How should we adapt to make the most of the amount available to us,
when the price of x is $ 20, while the price of y is $ 45?
b) New tax rules means that the price of x increases to $ 30, while the price of y remains
unchanged. What then becomes the adjustment?
A type of building element shall be produced where the sides of the foundation are x and 2x
and the height is y.
a) Show that the surface and volume of the element are A=4x2 +6xy and V=2x2
b) The element must have a specific weight and thus a specific volume. The volume should be
Since the element is to be surface treated, it should have as little surface as possible.
Determine x and y so that A gets the smallest possible value.
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