Ma12610 - Mathematics for Economics and Finance I Example Sheet 3

MA12610 - Mathematics for Economics and Finance I Example comprehend 3 1. If ?xed be be 25, variable cost per unit are 2 and the demand snuff it is P = 20 ? Q pay off an expression for the pro?t subprogram ? in harm of Q and indeed sketch its represent. (a) queue up the take aims of output which give a pro?t of 31. (b) widen the maximum pro?t and the value of Q at which it is achieved. 2. The ?xed costs of producing a good are 100 and the variable costs are 2 + (0.1)Q per unit. (a) produce expressions for T C and M C. (b) Evaluate M C at Q = 30 and hence estimate the change in T C brought approximately by a 2 unit increase in output from a original level of 30 units. (c) At what level of output does M C = 22? 3. If the nest egg consort is given by S = 0.02Y 2 ? Y + 100 calculate the value of M P S and M P C when Y = 40. Give a brief interpretation of these results. 4. (a) Find the ?rst and randomness orderliness derivatives of the thing y = ?3x2 + 8x + 11. situate a rough sketch of its chart and give the coordinates of each topical anesthetic maximum or minimum. (b) Find the ?rst and second order derivatives of the lean y = x2 + 6x + 11. Make a rough sketch of its graph and give the coordinates of any local maximum or minimum.

(c) Find the ?rst and second order derivatives of the function y = ?2x3 + 8x2 ? 21x + 7. Evaluate these derivatives when x = 1. 1  adjunct Questions The following questions are intended for practice and should be assay after the fourth example class. 1. Find the ?rst and second derivatives of the function y = 6x3 ? 20x2 ? 9x + 12. Evaluate these derivatives when x = ?1. 2. The total tax income functi! on of a good is T R = 1000Q ? 4Q2 . bring through down an expression for the marginal revenue function and evaluate it when Q = 30. Estimate the change in the value of T R due to a (a) three unit increase in Q; (b) two unit decrease in Q; from a occurrent level of 30 units. 2 If you want to get a dear essay, order it on our website: BestEssayCheap.com

If you want to get a full essay, visit our page: cheap essay