# Math Problems

## Transcribed Text

TASK 4 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? TASK 5 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 y rrespectively b) The element must have a specific weight and thus a specific volume. The volume should be 72 (dm3 ). 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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