Considering the constraint in processing, which combination of Products A and B maximizes the total contribution margin? a.40 units of A and 20 units of B b. 60 units of A and 0 units of B c. 80 units of A and 0 units of B d. O units of A and 40 units of B e. O units of A and 60 units of B
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- #1- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements and available resources for each lot of pens are given in the following table: Fliptop Model Tiptop Model Available Plastic 3 4 36 Ink Assembly 5 4 40 Molding Time 5 2 30 The profit for either model is $1,000 per lot. a) What is the linear programming model for this problem? b) Using Microsoft Excel's Solver, find the optimal solution. How many Fliptop models and how many Tiptop models should be produced? What is the maximum profit? c) Will there be excess capacity in any resource? Use Excel's Solver and run a sensitivity report to answer the following questions. d) Over which range can the objective function coefficient for Fliptop Models change without affecting the original optimal solution? What is this range called? e) What is the shadow price (dual price) for the plastic constraint and how would you interpret it? f) What is the shadow price (dual price)…Solve the problem using Linear programming model formulations, slack variables, and graphical solutions to determine the optimal product mix that will maximize profit. A company produces two products,A and B, which have profits of 9.00 in product A and 7.00 in product B. Each unit of product must be processed on two assembly lines, where the required production times are as follows Hours/unit Product Line 1 Line 2 A 12 4 B 4 8 Total Hours 60 40 What would be the effect on the optimal solution if the profit for product B was increased from 7.00 to 15.00? Solve with graphical solutions. What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours? Solve with graphical solutions.Ann and Ben are getting divorced and want todetermine how to divide their joint property: retirementaccount, home, summer cottage, investments, and miscellaneous assets. To begin, Ann and Ben are told to allocate100 total points to the assets. Their allocation is as shownin Table 69.Assuming that all assets are divisible (that is, a fractionof each asset may be given to each person), how should theassets be allocated? Two criteria should govern the asset allocation:Criteria 1 Each person should end up with the same number of points. This prevents Ann from envying Ben and Benfrom envying Ann.Criteria 2 The total number of points received by Ann andBen should be maximized.If assets could not be split between people, what problemarises? TAB LE 69PointsItem Ann’s Ben’sRetirement account 50 40Home 20 30Summer cottage 15 10Investments 10 10Miscellaneous 5 10
- ou are given a linear programming problem. Maximize P = 3x + 3y subject to 5x + 3y ≤ 30 Resource 1 2x + 3y ≤ 21 Resource 2 x ≤ 4 Resource 3 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 3y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.The north-south highway system passing through Albany, New York can accommodate the capacities shown in the table below. From To Capacities 1 2 3 1 3 6 1 4 3 2 4 2 2 5 4 3 4 3 3 6 2 4 2 2 4 3 3 4 5 2 4 6 3 5 2 4 5 4 2 5 6 6 How many units go from Node 1 to 3 and 4 to 2, respectively, in order to maximize the flow. a. 5 and 1. b. 5 and 2. c. none of the answers proposed apply d. 6 and 1. e. 6 and 2.Amy Zeng, owner ofZeng's Restaurant Distributions,supplies nonperishable goods to restaurants around the metroarea. She stores all the goods in a storage area with a single dockand one aisle. The goods are divided into five categories accordingto the following table. The table indicates the number of tripsper month to store or retrieve items in each category, as well asthe number of storage blocks taken up by each. The following picture of the storage area provides an identificationnumber for each of the 16 storage blocks. For each item category,indicate into which blocks it should be stored.
- Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. d) If 10 hours less of labor time were available, what would the values of the decision variables be? The objective function? Explain. e) If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated? f) If profit per unit on each…2) A farmer is planning the crops that will be planted in the upcoming season. The farmer can get $353.08 per metric ton of soybean, $119.42 per metric ton of barley, $163.80 per metric ton of corn, and $212.64 per metric ton of wheat. The total capacity of the farm is 400 metric tons of product. Based on rising tariffs, at most, the soybeans should constitute 20% of the total crop. Prices for barley and wheat have been declining, so corn should at least be 175 metric tons. a. Solve the linear program using Solver and write the strategy. b. Run a sensitivity analysis and identify the constraints that are binding. c. What is the change in the objective function value if the minimum for corn was 100 metric tons and the farmer acquired land that could produce 75 more metric tons of crop? Please show work in excelSuppose Jack like to solve the following formulation in Excel. And the problem is setup in Excel like this: See attached picture. A B C D E 1 X1 X2 2 decision variable objective 3 coefficient of objective function 2 3 4 Constraints LHS RHS 5 Constraints 1 2 1 3 6 Constraints 2 4 5 20 7 Constraints 3 2 8 16 8 Constraints 4 5 6 60 We want to put our objective function in cell D3. What should we type in D3? In cell D5 to D8, we will put the left hand side of our constraint. What should we type in D8? In OpenSolver, what should we assign to Variable Cell? What should you do to input the non-negativity constraint in OpenSolver?
- Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pen...Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for each lot of pens are given below.Fliptop Model Tiptop Model AvailablePlastic 3 4 36Ink Assembly 5 4 40Molding Time 5 2 30The profit for either model is $1000 per lot.What is the linear programming model for this problem?What are the boundary points of the feasible region?What is the profitability at each boundary point of the feasible region?Find the optimal solution.Explain all the steps when implementing the Branch and Bound method for the following optimization problem: Max 15*x1+12*x2+4*x3+2*x4 s.t. 8*x1+5*x2+3*x3+2*x4 <=10 3*x1+2*x3<=4 x1, x2, x3, x4 binarydevelope a space matrix for macdonalds. Below are the instructions. The steps required to develop a SPACE Matrix are as follows: 1. Select a set of variables to define financial position (FP), competitive position (CP), stability position (SP), and industry position (IP). 2. Assign a numerical value ranging from +1 (worst) to +7 (best) to each of the variables that make up the FP and IP dimensions. Assign a numerical value ranging from -1 (best) to -7 (worst) to each of the variables that make up the SP and CP dimensions. On the FP and CP axes, make comparison to competitors. On the IP and SP axes, make comparison to other industries. 3. Compute an average score for FP, CP, IP, and SP by summing the values given to the variables of each dimension and then by dividing by the number of variables included in the respective dimension. 4. Plot the average scores for FP, IP, SP, and CP on the appropriate axis in the SPACE Matrix. 5. Add the two scores on the x-axis and plot the resultant…