Use the method of linear programming to solve the problem.A craftswoman produces two products: floor lamps and table lamps. Production of one floor lamprequires 75 minutes of her labor and materials that cost $25. Production of one table lamp requires 50minutes of labor, and the materials cost $20. The craftswoman wishes to work no more than 40 hourseach week (2400 minutes each week), and her financial resources allow her to pay no more than $900for materials each week. If she can sell as many lamps as she can make and if her profit is $39 per floorlamp and $33 per table lamp, how many floor lamps and how many table lamps should she make eachweek to maximize her weekly profit? What is the maximum profit?Step 4: Graph the region of possible solutions (by finding the x and y intercepts for each inequality, orany two points for vertical and horizontal inequalities.).

Floor LampTable LampAvailable Labour75502400Material 2520900Profit3933Let x and y be the number of…

Answered: Use the method of linear programming to…

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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Micah's gym is moving into a bigger space, where he can have more stationary bicycles and treadmills in his gym. Let x be the number of treadmills and y be the number of bicycles. The number of new bicycles must be more than 1/3 times the number of new treadmills. Each bicycle costs $340 and each treadmill costs $670. He must spend less than $5,650. Select ALL the constraints for this situation. 1.) 670x + 340y 0 3.) x > 0 4.) x > 1/3y 5.) 670x + 340y < 5650 6.) y > 1/3x
Formulate but do not solve the problem.The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $44 and $28 per acre, respectively. Jacob Johnson has $17,200 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? (Let x and y denote the number of acres of corn and wheat, respectively.) = 500 = 17,200
Linear programming model
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200, and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. What are the binding constraints of the feasible region of the optimal solution? Constraint 2 only Constraint 1 only…
A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? I need to use the Five Step Method for mathematical modeling. Ask the Question. The Question must be phrased mathematically and object must be stated in precise mathematical terms. List all variables and assumptions you are making about them. Do not confuse variables with constants in the problem. Check units for consistency. Select a modeling approach. This could be optimization in one or more variables, linear programming, or many other approaches available in the field of math. Formulate the model. Restate…
A farmer in the magical land of Avalon is raising a unicorn to sell to a band of Jewel Riders. The market price for unicorn is $12 per pound, but is falling 10 cents per day. The rapidly growing unicorn is currently weighing 400 pounds and is expected to gain 5 pounds per day for the next two to three weeks. The costs to raise a typical unicorn are $5 per day plus $100 for a special unicorn harness and feedbag. What is the optimal time to sell the unicorn to the Jewel Riders? P(x)= -.5x2+15x+4700 P'(x)= -x+15 p"(x)= -1 < 0 SENSITIVITY ANALYSIS: (This is the part I am a bit uncertain about. The questions below.) Any help is much appreciated. 1. Preform a sensitivity analysis of the optimal time to sell versus the variable cost to raise a unicorn (harness still $100). 2. So if the actual variable cost was $4.00 per day instead of $5.00 (20% decrease), what would you estimate for the best time to sell based on your sensitivity results? 3. Finally, substitute $4.00 for the variable…

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