3. (parts a to e) Suppose that total oil reserves are known to be 100 units. For planning purposes, the world can be divided into three periods (t = 0, 1 and 2). The inverse demand curve for oil in the three periods is given by: Pt= 100 – qt The marginal extraction cost is $10 and the discount (interest) rate is 10%. a. Write down the socially optimal (dynamically efficient) allocation problem. b. Calculate the dynamically efficient quantities extracted and the prices in each period. c. Find the shadow price of the oil reserves and the MUCS. d. Is Hotelling's rule satisfied? Explain by including a definition of this rule. e. If new exploration prove that the current reserves is more than it was believed and it is 350 units how your solutions to parts b and c change?

3. Masagana Electronics, a firm that manufactures affordable microcomputers, is about to start production of two new types of microcomputers: VOICE and ECHO. Each type will require assembly time, inspection time and storage space. The amounts of the resources that can be allocated to the production of the microcomputers are limited. The manager of the firm would like to know the quantity computer to produce to maximize profit. The data are given below: VOICE ECHO 10 hours 4 hours 1 hour 2 hours Storage Space per unit 2 cubic feet P2,850 2 cubic feet P2,800 Profit per unit a. Formulate the linear program appropriate for this problem. b. Graphically illustrate the linear program. Label your axes properly and shade the feasible region. c. How many units of each type of computer should the firm produce to maximize profit? Available 100 hours. 22 hours 26 cubic feet Assembly Time per unit Inspection Time per unit

b.A clothing manufacturer makes trousers, skirts and blouses. Each trouser requires 20 minutes of cutting time, 60 minutes of sewing time and 5 minutes of packaging time. Each skirt requires 15 minutes of cutting time, 30 minutes of sewing time and 12 minutes of packaging time. Each blouse requires 10 minutes of cutting time, 24 minutes of sewing time and 6 minutes of packaging time. The amount of time available for cutting, sewing and packaging is 115 hours, 280 hours and 65 hours respectively. Using either the Inverse Method or the Cramer’s Rule, determine how many of each type of clothing should be made to use all available labor hours?

c) - X kboard.sanjac.edu/webapps/assessment/take/launch.jsp?course_assessment_id=_837122_1&course_id=_3235437_1&content_id=_3955990 ck- ES y ! 1 + F1 Question Completion Status: QUESTION 1 Alex has a budget of $100 a month for movie tickets and restaurant meals. A movie ticket will cost $10 and a restaurant meal costs $20. Which of the following combinations is part of Alex's budget constraint? O a. 2 movie tickets and 4 restaurant meals O b. 2 movie tickets and 5 restaurant meals O c. 2 movie tickets and 1 restaurant meal O d. 4 movie tickets and 4 restaurant meals @ 2 F2 QUESTION 2 Irfan has the budget constraint described in the graph below. If Irfan purchases 1 hour of tutoring per month and decides to increase his purchases to 2 hours per month, what is the opportunity cost of the 2nd tutoring hour? Irfan's Budget Constraint month 3 987 Click Save and Submit to save and submit. Click Save All Answers to save all answers. F3 # 3 0,8 Ox F4 $ 4 F5 % 5 F6 A 6 DELL F7 & 7 F8 * 8 F9 ( 9…