Suppose you have a bounded feasible region with corner points (0,7),(3,4),(9,1), and (12,0). Find the minimum of the objective function C=3x+4y on this feasible region, as well as where it occurs.

Consider a cheap talk game in which Nature chooses the sender’s type andthere are three feasible types: x, y, and z, which occur with probability 1/4, 1/4,and 1/2, respectively. The sender learns her type and then chooses one of fourpossible messages: m1, m2, m3, or m4. The receiver observes the sender’smessage and chooses one of three actions: a, b, or c. The payoffs are shown in the table below. a. Suppose the sender’s strategy is as follows: (1) if the type is x, thenchoose message m1, and (2) if the type is y or z, then choose messagem2. The receiver’s strategy is the following: (1) if the message is m1,then choose action a; (2) if the message is m2, then choose action b;and (3) if the message is m3 or m4, then choose action a. For appropriatelyspecified beliefs for the receiver, show that this strategy pair is aperfect Bayes–Nash equilibrium.b. Find a separating perfect Bayes–Nash equilibrium.

B & C

Consider a buying firm and a supplier negotiating terms for a contract.  Suppose the Marginal Benefit to the buying firm of additional contract provisions in a contract (x) to the firm is: MB = 20,000 – 400x. Suppose the Marginal Cost to the buying firm of additional contract provision to the firm is: MC = 100x. What is the optimal number of contract provisions? Reconsider the previous question. If the maximum value (or price) of the contract that the buying firm is willing to pay for is $3,000, what would you expect the firm to do? a) Use the spot market b) Vertically integrate c) Continue to contract d) engage in holdup

Determining Margin Potential Finding the maximum amount of profit you can generate from one unit of a product is called Margin Potential. This is useful for a company when making a decision about whether to go into production or not. In its simplest form, you can calculate Margin Potential as: Margin Potential = Maximum Price - Minimum Unit Costs Price Use the information table below to find the maximum price that customers deem acceptable. You can find this in the Customer Buying Criteria for each segment. Minimum Material Cost Calculate the minimum Material Cost per segment using the following equation and table below: Minimum Material Cost = [(Lowest Acceptable MTBF * 0.30) / 1000] + Trailing Edge Material Cost Minimum Labor Cost Calculate the minimum Labor Cost for each segment. Assume a base labor cost of $11.20 ($11.20 is a rough estimate of labor cost used solely to illustrate the Margin Potential Concept). Minimum Labor Cost = [$11.20 - (1.12 * Automation Ratings Below)] + 1.12…

Andy Mendoza makes handcrafted dolls, which he sells at craft fairs. He is considering mass producing the dolls to sell in stores. He estimates that the initial investment for plant and equipment will be  $10,000, while labor, material, packaging, and shipping will be about $8 per doll. He has determined that monthly sales volume is related to price, according to the following equation: v=5000-90p. Develop the nonlinear profit function as a function of price.