Math Exercises Problem Example | Topics and Well Written Essays - 1000 words

Activities - Math Problem Example 1 A firm makes and sells q units of an item at cost =  £(575 † ½ q) which has unit expenses of  £(q2 †25q) and fixed expenses of  £45,000. (a) Write down articulations for: income, benefit and normal expense as far as output(q) of the firm. [1 mark] Income = (575 † ½ q ) q = 575q † ½ q2 Benefit = Revenue †Total Cost = 575q † ½ q2 - [(q2 †25q )q +45,000] = 575q † ½ q2 †q3 + 25q2 - 45,000 = †q3 + 24.5q2 + 575q - 45,000 Normal Cost = Total Cost/q = q2 †25q + 45,000/q (b) Find articulations for: negligible income, peripheral cost, minor benefit and minimal normal expenses regarding yield (q). [2 marks] Peripheral Revenue, Marginal Cost, Marginal Profit and Marginal Average Costs is the subordinate of Revenue, Cost, Profit, Average Costs . Since the subordinate of f(x) = xn is nxn-1, we have: Minor Revenue = 575 †q Minor Cost = 3q2 - 50q Minor Profit = - 3q2 + 49q +575 Minor Average Cost = 2q †25 - 45,000/q2 (since 1/q = q-1) (c) Find the yield levels of the firm that and affirm that the yield levels found do to be sure expand or limit these functions [ 1 mark] (i) Maximise income †¢ This is the diagram of Revenue = 575q † ½ q2 , we can see that it is expanded at q = 575. (ii) Minimise costs To limit costs, set minor expenses to 0 q = 50/3 or approx 17 units This is the chart of Costs = q3 - 25q2 + 45,000. We can see that the limit esteem is around at q =17. (iii) Maximize benefits To boost benefits, set minor benefits to 0 - 3q2 + 49q +575 = 0 Utilizing the quadratic recipe, we have: q = 23.23 , - 7.89 Ignoring the negative worth, we have: q = 23 units. This is the chart of Profit = - q3 + 24.5q2 + 575q - 45,000. We can see that the greatest worth is around at q=23. (iv) Minimize normal expenses To limit normal costs, set peripheral normal expenses to 0: 2q - 25 - 45,000/q2 = 0 (multiply the two sides by q2) 2q3 - 25q2 - 45,000 = 0 With the utilization of experimentation, we get the main conceivable incentive as: q = 33 units. This is the diagram of Average Cost = q2 - 25q + 45,000/q. We can see that the most extreme worth is roughly at q=33. 2. The interest work for an item is given by the accompanying articulation: q = 25 + 200 (p - 2) (a) Calculate the interest at costs 3 and 7 [1/2 imprint ] For p = 3: q = 25 + 200 (3 - 2) q = 25 + 200 q = 225 For p = 7: q = 25 + 200 (7 - 2) q = 25 + 40 q = 65 Answer in (Q,P) structure: (225,3), (65,7) (b) Calculate the ARC versatility of interest regarding cost between the costs given to some extent (an) and remark on whether request is versatile or inelastic between these prices. [1/2 mark] Earc = (Q2-Q1)/[(Q2+Q1)/2] (P2-P1)/[(P2+P1)/2] Earc = (65-225)/[(65+225)/2] (7-3)/[(7+3)/2] Earc = - 160/145 4/5 Earc = - 40 = - 1.38 29 Since a versatile great is the place value flexibility of interest is more prominent than one, we can consider that the interest is versatile between these costs. (c) Find an articulation for POINT versatility of interest with deference to cost regarding price. [ 1 mark] Ept = (q/p) * p/q The subordinate of q = 25 +200/(p-2) is q/p = 0 + - 1 (200) (p-2)- 2 Also, q = 25 +200/(p-2) Henceforth: Ept = [-200p/(p-2)2]/[25 +200/(p-2)] (d) Calculate POINT versatility of interest at costs 3 and 7 and remark on their qualities and on the connection between Circular segment and POINT elasticity [1/2 mark] Ept = [-200p/(p-2)2]/[25 +200/(p-2)] Ept (3) = (- 600/1)/225 = - 2.67 Ept (7) = - 56/65 = - 0.862 The estimation of circular segment flexibility is in the middle of the estimation of point versatility which is normal