6. A drug company produces a drug from two ingredients, each ingredient contains same three antibiotics in different proportions. Each ingredient 1 produced results in P80 in cost; each ingredient 2 results in P50 in cost. The production of the antibiotics is dependent on the availability of limited resources, The resource requirements ( in grams) for the production are as follows: Antibiotic Resources requirement Minimum requirement Ingredient 1 Ingredient 2 1 3 1 1 4 2 12 The company wants to determine the number of grams of each ingredient 1 and 2 that must go in to drug in order to meet the antibiotics minimum requirements at the minimum cost.

6. A drug company produces a drug from two ingredients, each ingredient contains same three antibiotics in different proportions. Each ingredient 1 produced results in P80 in cost; each ingredient 2 results in P50 in cost. The production of the antibiotics is dependent on the availability of limited resources, The resource requirements ( in grams) for the production are as follows: Antibiotic Resources requirement Minimum requirement Ingredient 1 Ingredient 2 1 3 1 1 4 2 12 The company wants to determine the number of grams of each ingredient 1 and 2 that must go in to drug in order to meet the antibiotics minimum requirements at the minimum cost.

Name: 6. A drug company produces a drug from two ingredients, each ingredie
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Description: 6. A drug company produces a drug from two ingredients, each ingredient contains samethree antibiotics in different proportions. Each ingredient 1 produced results in P80 incost; each ingredient 2 results in P50 in cost. The production of the antibi

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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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
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.
A company that has cement factories in Denizli, İzmir and Uşak will transport the cements to theconsumption region 1, 2 and 3. The cement production capacities of the factories are 200 tons forthe factory in Denizli, 300 tons for the factory in İzmir and 450 tons for the factory in Usak.Demand of the first consumption region is 250, demand of the second region is 100, demand of thethird region is 225 and demand of fourth region is 325 tons of cement. The transportation costbetween factories and consumption areas is as below table per ton:Factories 1. Region 2. Region 3. Region 4. RegionDenizli 15 18 12 13İzmir 10 10 11 9Usak 8 5 7 8According to these data;1) Make the initial distribution of the enterprise according to the Vogel’s Approximation Method(VAM) and calculate the total transportation cost. 2) Determine the distribution that minimizes the total transportation cost according to the (MODI)method.
2- A multimedia company anticipates that there will be a demand for 20,000 copies of acertain DVD during the next year. It costs the company $0.40 to store a DVD for oneyear. Each time it must make additional DVDs, it costs $250 to set up the equipment.How many DVDs should the company make during each production run to minimize itstotal storage and setup costs?
Consider a labor market for men and women with two types of workers in each group, high ability (H types), and low ability (L types). H types among men and women have a productivity of 70 and L types among men and women have a productivity of 30. Among women 2/3rds are H types, and 1/3rd are L types, and among men ½ are H types, and ½ L types. Suppose affirmative action for women reduces the cost of college for all women to 10. What happens to the average wage gaps between men and women? Recall that employers know the shares of H and L types, but cannot observe individual types. ● Women on average make around 12% more than men. ● Women on average will make 40% more than men. ● Men will make 40% more than women. ● Women on average make 2/3rds more than men.
The Pretty Cat Company wishes to introduce a new brand of cat dry foods that meets certain nutritional requirements. The biscuit-1 contains 2 units of nutrient A and 4 units of nutrient B, while biscuit-2 contains 2 units of nutrient A and 2 units of nutrient B. According to federal requirements, there must be at least 80 units of nutrient A and 120 units of nutrient B in a package of the new dry food (biscuit mix). In addition, the company has decided that there can be no more than 30 biscuit-1 in a package. If it costs 2 cents to make a biscuit-1 and 4 cents to make a biscuit-2, what is the optimal product mix for a package of the new dry food in order to minimize the firm's cost? (a) Formulate this as a linear programming problem. (b) Find the optimal solution for this problem graphically. What is the total cost of a package of the new dry food using the optimal mix?
A grocery is supplied from 3 suppliers Fi(i = 1,2,3) who have: F1 of 5 trucks, F2 of 4 trucks and F3 of 6 trucks. The grocery is planned for a period of time, 12 trucks of goods. The transport from each supplier costs 40 monetary unitsfor F1, 60 monetary units for F2, respectively 50 monetary units for F3. Establish a supply schedule from the three suppliers so that the total cost of transport is as low as possible(minim cost). Observation: This is a linear program problem, i need only the mathematical model without solutions for the system, i only need those inequations.
3.3 4.manufactures 37-in. high def LCD tvs in 2 separate locations, Locations I and II. The output at Location I is at most 6000 televisions/month, whereas the output at Location II is at most 5000 televisions/month. TMA is the main supplier of tvs to the Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 4000 televisions to be shipped to two of its factories located in City A and City B, respectively. The shipping costs (in dollars) per television from the 2 TMA plants to the 2 Pulsar factories are as follows. To Pulsar Factories From TMA City A City B Location I $7 $3 Location II $8 $9 TMA will ship x televisions from Location I to city A and y televisions from Location I to city B. Find a shipping schedule that meets the requirements of both companies while keeping costs to a minimum. (x,y)= What is the minimum cost? 6.Solve the linear programming problem by…
The MPS for product A calls for 100 units to be completed in week 4 and 200 units in week 7 (the lead time is one week). Spare part demand for Item B is 10 units per week. Item B: Lot sizing rule: FOQ=500 Lead time (wks): 2 Beginning (on-hand) inventory: 100 Scheduled receipts: none Item C: Lot sizing rule: LFL Lead time (wks): 3 Beginning (on-hand) inventory: 10 Scheduled receipts: 200 (week 2) Develop a material requirement plan for the next 7 weeks for items B and C. What would be the impact of a scheduled receipt of 200 units for item B in week 2 (and all other data remained the same) on your calculated planned order receipts and releases?
An existing mall (Circuit Mall) is located near the residential area and has the following characteristics: Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) Circuit Mall 2.1 220 Three malls are to be built to rival the existing mall and there are currently three proposals. A total of 5000 shopping trips are generated from the residential area. Use n=1.5 Shopping Center Distance from residential area of Zone A (miles) Commercial Floor Space (thousand ft2) SM City 1 3.25 150 SM City 2 5.68 300 SM City 3 6.75 600 How many trips would Circuit Mall make compared to the new competitors?
Sametronics, Inc., manufactures electronic component A at a cost of $3 and B ata cost of $1 per unit. The same components, however, can be purchased from themarket at $4 and $2, respectively. Assembly scheduling requires a minimum of2,000 units of product A and 4,000 units of product B per week. Both require thesame time of two mechanical processes of which there are no more than 6,000and 3,000 hours available each week. Under the stated conditions, shouldmanagement make or purchase each product and in what quantities? Solve theproblem by the simplex method.
Cecille Paper Company uses softwood and hardwood pulp as basic materials for producing converter-grade paper. Hardwood is 80% pulp fiber and 20% pulp binder, while softwood is 50% pulp fiber and 50% pulp binder. The cost per pound for hardwood and softwood is $.50 and $.40, respectively. The company s quality control expert specifies that in order for the product to meet quality standards, each batch must contain at least 12,000 pounds of pulp fiber and at least 6,000 pounds of pulp binder. Because of equipment limitations, the size of a batch cannot exceed 24,000 pounds. The Production Department recently received a new standard from the Cost Department, allowing $8,200 per batch. The production manager feels that this amount is too low, because such costs have never been less than $8,400. Required: Using the graphic method, determine the hardwood and softwood mix necessary to minimize the cost per batch.