b) The utility U(x,y) units of satisfaction form owning x units of commodity 1 and y units of commodity 2 is given by U(x, y) = 2xy + 8x + 3y + 15 units per day. Currently 27 units of commodity 1 and 12 units of commodity 2 are consumed. Use Calculus to estimate the change in utility if he adds 2 units of commodity 1 and removes 3 units of commodity 2.

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A: We have to differentiate partially to this equation:

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: