(a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 – 250p and his total cost function is C(q) = 500 + 0.2q. (1) Derive an expression, R(q) for Teddy J's total revenue curve. (11) Derive an expression, I(q) for Teddy J's profit function. (ii) Determine whether Teddy J's profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.
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Relevant Course Objectives:
1. Apply the knowledge of functions to problems involving, supply, demand,
production, revenue and cost.
2. Identify the appropriate functions, equations and sequences which are to be used
in problem solving in the Social Sciences.
3. Use solutions to linear, quadratic, exponential and logarithmic equations to
determine
4. Solve problems involving rates of change and marginal change by the use of
derivatives
5. Write a linear system of equations in matrix form as a simple way to represent
multiple linear equations before solving them using a matrix approach.
6. Find and classify extreme points of a function for the purpose of identifying what
represents a minimum, a maximum or a point of inflexion.
7. Determine continuity or discontinuity of a function throughout its domain, since
some functions are not defined for all real numbers.
8. Solve a system of simultaneous equations with 3 variables using matrix inversion
and the Cramer's Rule.
9. Compute and interpret the value of the derivative of a function
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