4. Suppose you are the only producer and consumer inthe economy and the only constraint you face is time.You produce a apple in an hour, if you do not make aproduction, you enjoy your time as a leisure time. Youderive utility from both consuming the apple andconsuming the leisure time. Suppose there are T hoursto be used for both leisure and production. Additionallysuppose that you are provided with m ( > 0 ) apple ineach day by the government. ( Consumption does nottake time)i) Please draw the budget constraint and budget set youfaceii) Suppose that you become able to produce two applesin an hour but the number of apple provided everydayby government dropped to m-2 ( m > 2). Could youplease draw budget set and budget constraint undernew settings? (This scenario is valid only for thisquestion)iii) Suppose that if you use h (< T) hours of leisure(MULeisure / MUapple ) = 1 and if you use more thanh hours for leisureIULeisure / MUapple ) < 1, and ifyou use less than h hours for leisure ( MULeisure /MUapple) > 1. Under this new information pleasediscuss whether the optimal leisure ( h* ) is less thanh, is equal to h or is greater than h ?(h* represents optimal leisure use, MULeisure is theMarginal Utility of Leisure and MUapple is MarginalUtility of Apple).

Answered: Image /qna-images/answer/249b5660-7636-4ca3-8c1f-1999db7b44d4.jpg

Answered: 4. Suppose you are the only producer…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The toy manufacturer in the prototype example is going to release two new toys in the market. These are the magical pink wand and the ultimate wooden sword that contributes 30 pesos and 50 pesos respectively in the total profit. The daily production input and the available supply is given below. Plastic Wood Labor Magical pink wand 3 Ultimate wooden sword 2 2 Availability 50 120 180 The manufacturer wants to determine the daily production schedule that will give them the maximum profit. i. Formulate the LP model for the problem ii. Solve the problem graphicall iii. If the objective function is changed to Max z =c,x, +c,x2, determine the range of 2 |that will keep the computed optimal solution to remain optimal. Give a logical answer.
The table below represents consumption along Edgar's budget constraint, with each row representing a possible consumption bundle. Edgar derives 50 unites of happiness from eating his first hot dog, 40 units for the recond hot dog, 30 unites for the third hot dog, and so on with added utility declining by 10 for each hot dog consumed. The first soda provides 30 unites and declines by steps iof 3 for each additional soda. Using this information identify the optional (highest utility) consumption for Edgar. Hot dogs Soda 0 10 1 8 2 6 3 4 4 2 5 0 a.) 2 hot dogs & 6 sodas b.) 1 hot dog & 8 sodas c.) 3 hot dogs & 4 sodas d.) 5 hot dogs & 0 sodas
A firm manufactures 2 products A and B. The profits are 5$ and 8$ respectively. The firm has 2 machines and below is the required processing time in hours for each machine on each product. Product A В Machines G 6. 8. H 4 Machine G must be operated for at least 48 hours. Hours Available for machine H is 20 hours. Set up an LP problem to maximize profit and solve it graphically.
Suppose demand is given by p = 1600 − x. Find the maximum revenue.
5) A factory owner has 100 employees that produce 6000 computers per day. For each additional employee that the owner highers, the average production per employee decreases by 8 computers. How many employees should the owner have in order to maximize production?
1- A walnut grower estimates from past records that if 20 trees are planted per acre, then each tree will average 60 pounds of nuts per year. If, for each additional tree planted per acre, the average yield per tree drops 2 pounds, then how many trees should be planted to maximize the yield per acre? What is the maximum yield?
6. (a) A man has $4.55 in change composed entirely of dimes and quarters. What are the maximum and minimum number of coins that he can have? Is it possible for the number of dimes to equal the number of quarters? (b) The neighborhood theater charges $1.80 for adult admissions and $.75 for children. On a particular evening the total receipts were $90. Assuming that more adults than children were present, how many people attended? (c) A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum is 114. How many of each were there originally?
4. A manufacturer must decide how many chairs and tables to produce in a given week. It takes 2 hours to construct a chair and 3 hours to construct a table. The finishing process requires 2 hours for each chair and 2 hours for each table. There are 36 work hours available for construction and 28 work hours available for finishing. If the profit is $15 per chair and $25 per table, how many of each should be produced to maximize profit? Define your variables. HO 8 Find the Profit or Objective Function. Construction Find the Constraint equations. Do negatives make sense? 61 y Pt d for chairs for tables ho 21139036 X20 10 12 14 1618002 2 PCXIT ISXH59 The vertices of the feasible region. y 20 finish 2x+2y ≤28 Y= y=-2 3X+12
(2) A retailer determines that the cost of ordering and storing units of a product can be modelled by
Example 12.8. A firm uses milling machines, grinding machines and lathes to pro- duce two motor parts. The machining times required for each part, the machining times avail- able on different machines and the profit on each motor part are given below : Machining time reqd. for the motor part Max. time available per Type of machine (mts) week (minutes) I II 10 2,000 Milling machines Grinding machines Lathes. 2 900 12 3,000 Profit/ unit (Rs.) 100 40 Determine the number of parts I and II to be manufactured per week to maximize the profit. د ه
Refer to the production possibilities curves for Chairland and Tableland. Chairland can produce 36 chairs per day and no tables, or 18 tables table per day and no chairs. Tableland can produce 40 chairs per day and no tables, or 40 tables per day and no chairs. If the two countries split the difference between the buyer's willingness to pay for tables and the seller's willingness to accept, in terms of the number of chairs for 1 table, the terms of trade will be . (Enter your response rounded to one decimal place.) Country Quantity per day Opportunity cost of chairs Opportuity cost of tables Tableland 40 chairs, 40 tables 1 table 1 chair Chairland 36 chairs, 18 tables 1/2 table 2 chairs
5. A small business enterprise makes dresses and trousers. To make a dress, it requires ½ hour of cutting and 20 minutes of stitching. To make a trouser, it requires 15 minutes of cutting and hour of stitching. The profit on a dress is N$40 and on a pair of trousers N$50. The business operates for a maximum of 8 hours per day Determine how many dresses and trousers should be made to maximize profit and what the maximum profit is. O A The maximum profit is N$800, 10 dresses and 8 trousers OB The maximum profit is N$850, 12 dresses and 6 trousers OC The maximum profit is N$860, 12 dresses and 6 trousers OD The maximum profit is N$880, 12 dresses and 8 trousers

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