Marginal Revenue from Polynomial Demand Model
A company faces a demand function given by \(p(x)=120-2x-0.5x^2\), where \(x\) represents the number of units sold. \n\n(a) Formulate the revenue function \(R(x)\) as the product of the number of units sold and the price function \(p(x)\). \n\n(b) Differentiate \(R(x)\) with respect to \(x\) to obtain the marginal revenue function \(R'(x)\). \n\n(c) Explain the economic […]
Revenue Function Optimization: Finding Intercepts & Maximum Revenue
A company models its daily revenue with the function \( R(x) = -2x^2 + 80x – 600 \), where \( x \) represents the number of items sold over a base level. Using a Graphing Display Calculator (GDC), find the x-intercepts of the revenue function and determine the maximum daily revenue. Clearly outline the steps […]
Optimizing Profit in a Multi-Factor Cost Model
A company manufactures electronic components. The production cost function is given by \(C(x) = 1000 + 20x + 0.1x^2\), where \(x\) represents the number of components produced. For orders larger than 200 units, the company applies a discount on the sale price. In this scenario, assume the effective sale price per unit is modeled by […]
Optimising Revenue with Linear Demand
A company faces a linear demand for its product given by \( p(x) = 100 – 2x \), where \( p(x) \) is the price in dollars when \( x \) units are sold. (a) Determine the revenue function \( R(x) \) in terms of \( x \). (b) Determine the number of units \( […]