PLEASE DO IT BY HAND ! Do not use excell Problem 2 Central Critical Chemical (CCC) manufactures three chemicals: A, B and C. Thesechemicals are produced via two production processes: 1 and 2.• Running process 1 for an hour costs $4 and yields 3 units of A, 1 unit of B, and 1 unit of C.• Running process 2 for an hour costs $1 and yields 2 units of A and 1 unit of B.To meet customer demand, at least 6 units of A, 3 units of B, and 1 unit of C must be produceddaily. Suppose you are asked to formulate an LP model for CCC to determine an optimal dailyproduction plan (i.e., how many hours should CCC run process 1 and how many hours should CCCrun process 2 each day) that minimizes the total cost.(a) Write down LP model and clearly define the decision variables, the objective function, andconstraints.(b) Solve the LP model using the graphical method.(c) Provide a justification on why the divisibility assumption holds for the problem.

Given: Central Critical Chemical manufactures three Chemicals A, B, and C which are produced via…

Answered: Problem 2 Central Critical Chemical…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 27EQ

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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.
2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
2. A firm produces two products A and B. Both products need to undergo a press machine and a paining process. Every unit of product A needs 40 hours of the press machine and 50 hours of the painting process. Similarly, every unit of product B needs 40 hours of the press machine and 25 hours of the painting process. Each unit of product A brings 600,000 yen of profit and every unit of product B 400,000 yen. Every month, the total available time for the press machine is 480 hours and for the painting process 400 hours. Formulate this problem as a LP model and solve the model.
Glueco produces three types of glue on two differentproduction lines. Each line can be utilized by up to sevenworkers at a time. Workers are paid $500 per week onproduction line 1, and $900 per week on production line 2.A week of production costs $1,000 to set up production line1 and $2,000 to set up production line 2. During a week ona production line, each worker produces the number of unitsof glue shown in Table 12. Each week, at least 120 units ofglue 1, at least 150 units of glue 2, and at least 200 units ofglue 3 must be produced. Formulate an IP to minimize thetotal cost of meeting weekly demands.
Example 6 (Diet problem): A dietician wishes to mix two types of foods in such a way that vitamin contents of the mixture contain atleast 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food 'II' contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to purchase Food 'I' and Rs 70 per kg to purchase Food 'II'. Formulate this problem as a linear programming problem to minimise the cost of such a mixture.
A company manufactures two, A and B, on two machines, 1 and 2. It has been determined that the company will realize a profit of $3/unit on Product A and a profit of $4/unit on product B. To manufacture 1 unit of Product A requires 6 min on Machine 1 and 5 min on Machine 2. To manufacture 1 unit product of Product B requires 9 min on Machine 1 and 4 min on Machine 2. There are 5 hr of machine time available on Machine 1 and 3 hr of machine time available on Machine 2 in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? What is the largest profit the company can realize? Is there any time left unused on machines?
Suppose you’ve designed two versions of your system (herein called “product A” and “product B”). The estimated profit for product A is $0.75 per unit and for product B is $0.65 per unit. To manufacture these products at your company, you’ll need to compete for internal resources. To manufacture a single unit of product A requires 5.0 minutes of machining, 2.5 minutes at a soldering station, and 1.5 minutes for final software testing. Product B requires 3.0 minutes of machining, 4.0 minutes at the soldering station and 2.0 minutes of software testing. The capacity of the machining department is 1,200 minutes per week, capacity of the soldering station is 800 minutes per week, and capacity of final software testing is 600 minutes per week. 1. To maximize profits based on the given constraints, how many of product A should be made per week? 2. To maximize profits based on the given constraints, how many of product B should be made per week? 3. What is the maximum profit when the…
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. The company will realize a profit of $4.50/unit of Product A and a profit of $4/unit of Product B. Manufacturing 1 unit of Product A requires 6 min on Machine I and 5 min on Machine II. Manufacturing 1 unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of time available on Machine I and 3 hr of time available on Machine II in each work shift. (a) How many units of each product should be produced in each shift to maximize the company's profit? The maximum is P = at (x, y) = ( (b) Suppose P = cx + 4y. Find the range of values that the contribution to the profit of 1 unit of Product A, the coefficient c of x, can assume without changing the optimal solution. scs (c) Find the range of values (in hours) that the resource associated with the time constraint on Machine I can assume. s (resource) s (d) Find the shadow price for the resource associated with the…
1. A company produces two colors of cloth, namely red and pink. In order to produce these colors, 2 special raw materials are being used by the company. The production data is given below: Meters of raw material per meter of Maximum daily availability Red Cloth Pink Cloth Raw Material 1 2 1 6 Raw Material 2 4 24 Profit per ton (1000) According to the dealer, the daily maximum demand for red cloth is 2 meters and the daily demand for red cloth can't exceed that for pink cloth by more than 1 meter. The company wants to maximize its daily profit. a. Construct the LP Model of this problem. b. Find the optimal solution using Graphs. (graphing paper or desmos) c. Find the optimal solution using Excel Solver. (Sheet 1) d. Find the optimal solution using Algebraic Solution. e. Find the optimal solution using the Simplex Method. (Not in excel)
1. A small refinery produces only two products: Super and Diesel. These are produced by processing crude oil through three (3) processors: a cracker, a splitter and a separator. To produce one barrel of Super requires 3 hours for cracker, 2 hours for separator and splitter requires three times the hours required for cracker. To produce a barrel of Diesel requires 4 hours for splitter, half the time required for splitter is needed for cracker and five times the time required for cracker is needed for separator. The factory has allocated at most 66 hours for cracker, 180 hours for splitter and 200 labour hours for separator. In addition, it cost the producer GHC45.00 and GHC90.00 per barrel to produce Super and Dicsel respectively. Selling prices per barrel of Super and Diesel are GHC135.00 and GHC165.00 respectively. Formulate the manufacturer's problem as LP so as to maximize profit whilst satisfying the resource limitation. b. Determine how many of each item should be produced to…
5. Next Monday, Concrete Co need to supply concrete to four different building sites. They prefer to use plants 1 and 2 for the production and delivery of the concrete, because they are quite close to the sites, but find it necessary to use plant 3 to satisfy the rest of the demand. The table below shows supply and demand amounts in tonnes, and cost coefficients in $ per tonne. Cij Site 1 70 40 130 75 Plant 1 Plant 2 Plant 3 Demand Site 2 40 50 210 23 Site 3 20 30 80 19 Site 4 50 60 90 25 Supply 80 55 7 Concrete Co wish to minimise their total cost. Treat this as a primal LP problem. (a) Show that Concrete Co have balanced their transportation problem. (b) Use the Least Cost Method to find a basic feasible solution to this primal problem. Verify that you have the correct number of basic variables. [Hint: You should look at 13 first. Then 12 and 21 are both contenders, but it does not matter what order you choose them in.] (c) Use complementary slackness conditions to find a dual…

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