Consider the following situation:A company that operated 10 hours a day manufactures two products on three sequential processes.Which of the following accurately shows the constraint on the daily capacity forthe first production process?Product2Process 110Process 220Process 3810Unit Profit2030A. 10x + 5y s 10B. 10x + 5y s 600C. 10x + 5y 2 10O D. 10x + 5y 2 600Which of the following is the most appropriate objective function for the givensituation?Product2Process 110inProcess 220Process 310Unit Profit2030a. Maximize 30x + 20yb. Maximize 20x + 30yc. Minimize 30x + 20yd. Minimize 20x + 300minutesminutes

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Answered: Consider the following situation: A…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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.
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…
Consider the following model of a monopolistic form, where P is the sale price of the good, MC is marginal cost of producing the good and q is quantity produced (assumed equal to quantity sold) the firm has to sell all units of the good at the same price. p=10-2q MC=2+q If the firm produces 3 units, what total revenue will it receive? a. £4 b. £6 c. £12 d. £24
need comprehensive and correct answers.This question is about optimization.
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QUESTION 7 A company manufactures two types of toys: T1 and T2 using the machines A, B and C. The time required to make T1 is 6, 8 and 12 hours in A, B and C respectively. The time required to make T2 is 8, 4 and 4 hours in A, B and C respectively. The maximum available times for the machine A, B and C are 380, 300 and 404 hours respectively. The profits on T1 and T2 toys are 5 and 3 OMR respectively. Let x = number of toys (T1); y = number of toys (T2). The constraint for the time on machine Ais 8x + 6y ≤ 380 6x + 8y ≥ 380 8x + 6y ≥ 380 6x + 8y ≤ 380
A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: Chemical P costs $100 a unit and chemical R costs $400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $80,000. 2= 100p0.8.0.2 A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units
(b) Let xij be the amount shipped from source i to destination j in a 5X5 transportation problem, and let Cij be the corresponding transportation cost per unit. The amounts of supply at sources 1,2,3,4 and 5 are 210, 150,250,190 and 150 units respectively and the demands at destinations 1,2,3,4 and 5 are 205, 220,180,180 and 165 units respectively. The cost of shipping from source 1 to destinations 1,2,3,4 and 5 are 29, 28, 31, 27 and 32 respectively. The cost of shipping from source 2 to destinations 1,2,3,4 and 5 are 26, 27, 30, 37 and 31 respectively. The cost of shipping from source 3 to destinations 1,2,3,4 and 5 are 32, 38, 29, 27 and 35 respectively. The cost of shipping from source 4 to destinations 1,2,3,4 and 5 are 33, 39, 27, 29 and 33 respectively. The cost of shipping from source 5 to destinations 1,2,3,4 and 5 are 35,31, 34, 23 and 35 respectively. (i)Find the associated optimal cost. (ii)Determine each non basic variable.
Consider the following model of a monopolistic form, where P is the sale price of the good, MC is marginal cost of producing the good and q is quantity produced (assumed equal to quantity sold) the firm has to sell all units of the good at the same price. p=10-2q MC=2+q If the firm produces 3 units, what will its total cost be? a. £5 b. £10.5 c. £8.25 d. £15

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