Solve the linear programming problem below by showing the graph of the feasible region and corner points. use DESMOS for this activity. A contractor builds storage sheds in two high end models, the Chelan and the Orondo. Each Chelan model requires: 2000 ft of framing lumber 6000 cubic feet of concrete $4000 for advertising Each Orondo model requires: 4000 ft of framing lumber 6000 cubic feet of concrete $6000 for advertising Contracts call for using at least 16000 ft of framing lumber, 36,000 cubic feet of concrete, and $30,000 worth of advertising. If construction cost for each Chelan shed is $40,000, and the construction cost for each Orondo shed is $30,000, how many of each model should be built to minimize construction costs?

A manufacturer of refrigerators must ship at least 100 refrigerators to its two warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 40 refrigerators already, while warehouse B has 15 on hand. It costs $10 to ship a refrigerator to warehouse A and $14 to ship one to warehouse B. How many refrigerators should be shipped to each warehouse to minimize cost?  Find the objective function and the constraints for the above problem.

2. Solve by Lagrange Multiplier Method: Clearly identify your constraint function and your system. You may use either approach you learned in class and on the video. Mr. Eppolito has S360 to spend on fencing to fence a rectangular garden. The fencing for the north and south sides of the garden costs $10/ft. The fencing for the east and west sides costs $15/ft. Find the dimensions that will allow Mr. Eppolito to fence in the largest-sized garden. Draw a diagram of this scenario. Write the method you will use to solve it, then do so, showing all the necessary equations.

Yang's Material Company hauls gravel to a construction site, using a small truck and a large truck. The carrying capacity and operating cost per load are given in the accompanying table. Yang must deliver a minimum of 120 cubic yards per day to satisfy his contract with the builder. The union contract with his drivers requires that the total number of loads per day is a minimum of 5. How many loads should be made in each truck per day to minimize the total cost? Capacity (yd³) Cost per Load Small Truck Large Truck 40 30 $90 $72 In order to minimize the total cost, the number of loads in a small truck that should be made is be made is. and the number of loads in a large truck that should

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…