Assignment Background: A Television Station Is Considering T ✓ Solved

Assignment background: A television station is considering the sale of

A television station is contemplating the sale of promotional DVDs and needs to determine the optimal way to produce these DVDs to maximize effectiveness and profit. The station can source the DVDs from two different suppliers, each offering distinct pricing and cost structures. Supplier A charges a set-up fee of $1200 plus $2 per DVD, while Supplier B has no set-up fee and charges $4 per DVD. The estimated demand for the DVDs is given by the function Q = 1 + P, where P is the price in dollars, and Q is the quantity demanded. The relationship between price and demand is defined by P = 8 - Q/200.

The primary objectives are twofold: first, to determine the quantity of DVDs the station should order when the DVDs are given away for free; second, to identify the optimal pricing and ordering strategy to maximize profit from sales, considering each supplier separately. The station aims to compare the maximum profits achievable with each supplier by applying the marginal revenue equals marginal cost (MR=MC) rule for each scenario. The marginal cost (MC) for each supplier corresponds to the additional cost incurred to produce one more DVD, which can be computed based on the suppliers' pricing structures.

The assignment requires solving two problems individually, one for each supplier, under the scenarios of free distribution and profit maximization. The calculations should include deriving the demand function, expressing revenue, identifying the marginal revenue, computing marginal costs, and finding the optimal quantity and price point. The analysis will facilitate a comparative evaluation of the profit potentials with each supplier to guide the station’s decision-making process.

Sample Paper For Above instruction

Introduction

Decision-making in business settings requires careful analysis of cost structures, demand functions, and profit maximization strategies. In the context of promotional DVD distribution, understanding the interplay between supplier pricing, fixed costs, and demand elasticity is essential. This paper explores the optimal production and pricing strategy for a television station considering two different suppliers, with tools rooted in economic theory, especially the marginal revenue equals marginal cost (MR=MC) principle. The analysis aims to provide actionable insights for maximizing profits and ensuring efficient resource allocation.

Demand and Revenue Analysis

The demand function provided is Q = 1 + P, which can be rewritten to express price as a function of demand: P = 8 - Q/200. This inverse demand function indicates that as the quantity of DVDs increases, the price the station can charge decreases slightly due to market saturation effects. To analyze optimal quantity and pricing, we must derive the total revenue (TR) and marginal revenue (MR).

Total revenue is TR = P × Q. Substituting the demand function into TR gives TR = (8 - Q/200) × Q. Expanding this, TR = 8Q - Q²/200. The marginal revenue is the derivative of TR with respect to Q: MR = d(TR)/dQ = 8 - Q/100.

Cost Analysis and Supplier Structures

For supplier A, the total cost (TC) to produce Q DVDs is TC_A = 1200 + 2Q. The marginal cost (MC) for supplier A is the derivative of TC_A with respect to Q: MC_A = 2. For supplier B, the total cost is TC_B = 4Q, and the marginal cost MC_B = 4.

Scenario 1: DVDs Given Away

When DVDs are given free, the station's goal is to determine the quantity Q that maximizes exposure, which effectively means setting Q as large as possible within demand constraints. Since price P = 0, demand becomes Q = 1 + 0 = 1. But the demand formula suggests more DVDs could be sold at a positive price. For free distribution, the station should produce the maximum demand quantity that the market can handle. To find this, set P = 0 in the price demand equation, which yields Q = 8 - 0 = 8. Hence, the station should order 8 DVDs when distributing freely.

Scenario 2: Profit Maximization

When seeking profit maximization, the station should set MR = MC for each supplier and find optimal Q and P.

For Supplier A (MC = 2):

Set MR = MC: 8 - Q/100 = 2 → 8 - Q/100 = 2 → Q/100 = 6 → Q = 600.

Calculate the corresponding price: P = 8 - 600/200 = 8 - 3 = 5 dollars.

Revenue at this quantity: TR = P × Q = 5 × 600 = 3000 dollars.

Total cost: TC_A = 1200 + 2 × 600 = 1200 + 1200 = 2400 dollars.

Profit: π_A = TR - TC_A = 3000 - 2400 = 600 dollars.

For Supplier B (MC = 4):

Set MR = MC: 8 - Q/100 = 4 → 8 - Q/100 = 4 → Q/100 = 4 → Q = 400.

Corresponding price: P = 8 - 400/200 = 8 - 2 = 6 dollars.

Revenue: TR = 6 × 400 = 2400 dollars.

Total cost: TC_B = 4 × 400 = 1600 dollars.

Profit: π_B = 2400 - 1600 = 800 dollars.

Summary and Comparison

In the profit-maximizing scenario, sourcing from supplier B yields a higher profit ($800) compared to supplier A ($600). For free distribution, the station should order 8 DVDs, which is feasible within the demand constraints. These results highlight the importance of analyzing fixed and variable costs, demand elasticity, and setting optimal prices to maximize revenue and profit. The decision to choose a supplier hinges on these calculated profit margins, emphasizing the need for comprehensive economic modeling in procurement strategies.

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