Formulate but do not solve the following exercise as a linear programming problem. A financier plans to invest up to $400,000 in two projects. Project A yields a return of 10% on the investment of x dollars, whereas Project B yields a return of 13% on the investment of y dollars. Because the investment in Project B is riskier than the investment in Project A, the financier has decided that the investment in Project B should not exceed 40% of the total investment. How much should she invest in each project to maximize the return on her investment P in dollars?

Formulate but do not solve the following exercise as a linear programming problem.A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3 on each unit of Product A and $5 on each unit of Product B. To manufacture a unit of Product A requires 5 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 5 min on Machine II. There are 269 min available on Machine I and 205 min available on Machine II in each work shift. How many units of a product should be produced in each shift to maximize the company's profit P in dollars? Maximize      P  =             subject to the constraints Machine I             Machine II                     x ≥ 0         y ≥ 0

Just make the linear programming model of the next exercise: A company manufactures and sells two lamp models L1 and L2. For its manufacture, a manual work of 30 minutes is needed for the L1 model and 45 minutes for the L2, and a machine work of 25 minutes for L1 and 15 minutes for L2. 150 hours per month are available for manual work and 120 hours per month for the machine. Knowing that profit per unit is $150 and $100 for L1 and L2 respectively, plan production to maximize profit. Please be as clear as possible and show all the steps. Thank you very much

Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize      P  =             subject to the constraints board feet             labor-hours                     x ≥ 0         y ≥ 0

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…

Formulate but do not solve the following exercise as a linear programming problem.TMA manufactures 37-in. high-definition LCD televisions in two separate locations: Location I and Location II. The output at Location I is at most 6500 televisions/month, whereas the output at Location II is at most 5300 televisions/month. TMA is the main supplier of televisions to Pulsar Corporation, its holding company, which has priority in having all its requirements met. In a certain month, Pulsar placed orders for 3000 and 3600 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 two TMA plants to the two Pulsar factories are as follows.   To Pulsar Factories From TMA     City A     City B Location I $6 $4    Location II $8 $7    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…

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…