02 May QuestionBusiness Calculus – Assignment # 2Due April 11, 2019
Question
Business Calculus – Assignment # 2
Due April 11, 2019
Presentation of Assignment:
· Assignments are to be submitted on the stated date unless otherwise communicated.
· Late assignments will be accepted three (3) days after the due BUT the candidate cannot get more than 40%
· Assignments that are more than Three (3) days late WILL NOT BE ACCEPTED
· Assignments should be typed or neatly written.
· Assignments MUST have a TYPED cover page with the following.
· Name of Institution and campus
· Candidate’s name
· Candidate’s identification number
· Date of submission.
1. The cost of producing x mp3 players is calculated using the this formula that was developed by the company’s marketing staff
(a) Find the marginal cost function and find its value when 100 mp3 players are produced. (5 marks)
(b) Find the average cost function and estimate (5 marks)
(c) Determine the average change of cost from x = 100 to x = 125. (5 marks)
Total 15 Marks
2. (a) The fixed cost of production of a firm is $800, and the marginal cost is: C/x) = 0.03×2 + 0.12x + 5. Find the cost function. (5 marks)
(c) A manufacturer of electronic sphygmomanometers determines that the demand function for his product is given by: , and the supply function by: . The price p is in dollars and the number of units produced is x. If market equilibrium prevails, determine:
(i) the equilibrium price (4 marks)
(ii) the consumers’ surplus (3 marks)
(iii) the producers’ surplus. (3 marks) Total 15 Marks
3. (a) A ball is rolled up sloping ramp and after time, t, its distance from the starting point is given by the formula, . Calculate the furthest distance up the sloping ramp the ball travels? (4 marks)
(b) Find the coordinates of the turning point of the function and state whether it is a maximum or a minimum point. (5 marks)
(c) Find the integral of the following
(i) (2 marks)
(ii) (4 marks) Total 15 Marks
2
()25
dxx
=-+
()210
sxx
=+
3
2
4032
3
x
yxx
=+-+
(325)
xdx
–
ò
4
2
2
(6)
3
xdx
x
+
ò
2
()1000400.01
Cxxx
=++
()
Cx
–
(100)
C
–
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