Mathematics, 02.07.2020 14:01 myiacoykendall
1. A company estimates that if x thousand cedis is spent on the marketing of a certain product, Q(x)
thousand units of the product will be sold, where Q(x) = 7x / 27 + x²
(a) Determine the domain of the function defined. [2 Marks]
(b) Determine how much of the product will be sold if the company does not spend any money on
marketing. [2 Marks]
(c) Determine the amount of money the company must spend on marketing to achieve the minimum
and maximum quantities. Leave your answers to 2 decimal places. [10 Marks]
(d) Determine the maximum and minimum quantities that can be sold. Leave your answer to the
nearest whole number. [5 Marks]
(e) Determine the marketing expendure ranges on which quantity sold is increasing and decreasing
and interpret your solution. [9 Marks]
(f) Determine what happens as the company invests an infintely large amount of money on marketing.
[6 Marks]
(g) Use the information given from (a) to (f) to sketch the curve of Q(x). [6 Marks]
2. (a) The demand and supply functions of a particular good in a competitive market are defined
respectively as p = 200q
q1 and p = 30+2q. If p and q denote the price and quantity respectively,
determine the equilibrium price and quantity. [15 Marks]
(b) Let the price and quantity functions of a product be given by p = 2x + k and q = x + 2
respectively, where x is a variable and k is a constant. Find the value(s) of k for which the total
revenue function is always positive. [15 Marks
Answers: 2
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1. A company estimates that if x thousand cedis is spent on the marketing of a certain product, Q(x)...
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