# Assignment here answer all the questions in both

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Assignment instructions/requirements here Answer all the questions in both assignments Written work should be clear and legible Credit will only be given for logical and systematic presentation of solutions Correct answers without calculation steps will not attract full marks Avoid copying work from others as this may lead to nullification of assignment marks
TUTORIAL LETTER SEMESTER 1/2020 MATHEMATICS FOR ECONOMISTS 1A MFE511S 9 Question 1 (Derivatives and their applications) Total Marks: 38 1.1 Differentiate the following functions with respect to the independent variable. Ensure to use proper notation and simplify your final answers. Wrong notation will be penalised 1.1.1 6 2 5 5 3 2 1 3 ( ) x x x x f x x  [5] 1.1.2 2 4 3 ( ) x x f x e [5] 1.1.3 1 x x e y e [5] 1.2 Determine the first four derivatives of the function 2 ( ) 3 8 t R t t t e [4] 1.3 The sales (in 100 thousands N\$) of tickets of a recently premiered movie t years from the date of release is given by: 400 ( ) 100 5 f t t t 1.3.1 Find the rate at which the sales are changing at time t [5] 1.3.2 How fast are the sales changing at the time the movie was released (t = 0)? [3] 1.3.3 How fast are the sales changing 5 years from the date of release ( t = 5)? [3] 1.3.4 Comment on your results from 1.3.2 and 1.3.3 [2] 1.3.5 Are the rates of sales increasing or decreasing as the years progress? Confirm your answer using derivatives [6] Question 2 (Partial Derivatives and their applications) Total Marks: 23 2.1 If 3 3 2 3 z x y x y , show that 3 z z x y z x y [6]
TUTORIAL LETTER SEMESTER 1/2020 MATHEMATICS FOR ECONOMISTS 1A MFE511S 10 2.2 Consider the Cobb-Douglas production function for engineers (E) and technicians (T) given by 0.6 0.3 10 Q E T If the firm employees an equal number of engineers and technicians, how many technicians will it take to do the work of one engineer? Explain your result [9] 2.3 Determine dz dx given 3 2 5 2 2 3 5 4 x z xy z y x y [8] Question 3 (Integration and its Applications) Total Marks: 19 3.1 Determine the following integrals: 3.1.1 3 2 2 4 1 x x x dx x [6] 3.1.2 3 2 2 x e dx [4] 3.2 The revenue and cost rates of an mining exploratory company are 1 2 ( ) 14 R t t and 1 2 ( ) 2 3 C t t respectively, where the time 𝑡 is measured in years and ? and 𝐶 are measured in millions of dollars. 3.2.1 How long should the exploration be continued in order to obtain the maximum profit? [2] 3.2.2 Calculate the maximum profit for this company. [7] TOTAL MARKS FO ASSIGNMENT 02: 80 MARKS END OF TUTORIAL LETTER

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• Milly, Introductory Mathematical Economics, Alpha C. Chiang, Ms. Susan Mwewa, Ms. S Mwewa

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