Exercises - Management Accounting Concepts and Techniques for Decision Making 16. The Call Company has an available 120 pieces of material M1 and 80 meters of material M2 to produce its products A and B: Product A Product B Unit Contribution Margin Required Materials: Material M1 Material M2 P3 P4 2 pieces 4 meters 5 pieces 2 meters REQUIRED: a. Objective function - involving maximization of the company's contribution margin. b. Non-negativity constraint for the decision variables c. Constraint function for Material M1 d. Constraint function for Material M2 e. Optimal product mix
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- If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.Given the following information for a product-mix problem with three products and three resources. Primal Decision Variables: x1 = number of unit 1 produced; x2 = # of unit 2 produced; x3 = # of unit 3 produced Primal Formulation:Dual Formulation: Max Z (Rev.) = 25x1 + 30x2 + 20x3Min W = 50π1+ 20π2+25π3 Subject To8x1+ 6x2+ x3≤ 50(Res. 1 constraint)Subject To8π1+ 4π2+2π3≥ 25 4x1+ 2x2+ 3x3≤ 20(Res. 2 constraint)6π1+ 2π2+π3 ≥ 30 2x1+ x2+ 2x3≤ 25(Res. 3 constraint)π1+ 3π2+2π3≥ 20 x1, x2, x3≥ 0 (Nonnegativity)π1, π2, π3 ≥ 0 Optimal Solution: Optimal Z = Revenue = $268.75 x1 = 0 (Number of unit 1)Dual Var. Optimal Value = 22.5 (Surplus variable in 1st dual constraint) x2 = 8.125 (Number of unit 2)Dual Var. Optimal Value = 0 (Surplus variable in 2nd dual constraint) x3 = 1.25 (Number of unit 3)Dual Var. Optimal Value = 0 (Surplus variable in 3rd dual constraint) Resource Constraints: Resource 1 = 0 leftover…Maximize z= 5R+8P Subject to R+3/2P≤900 1/2R+1/3P≤300 1/8R+1/4P≤100 R,P ≥ 0 non-binding constraint: R+(3/2) P≤900 binding constraints: (1/8) R+(1/4) P≤100 and (1/2) R+(1/3) P≤300 redundant constraint R+(3/2) P≤900 1. What is the range of the coeficient, c1, of the decision variable R that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2 2. What is the range of the coeficient, c2, of the decision variable P that will make the optimal solution remain unchange? a. 13/3≤c1≤7 b. 10/3≤c1≤10 c. 4≤c1≤12 d. 13/2≤c1≤19/2
- Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 11 4 $B$3 Product_2 175 0 25 12 14 $B$4 Product_3 0 −1.5 25 8 5 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 multiple choice Product_1 Product_2 Product_3Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 10 5 $B$3 Product_2 175 0 25 10 14 $B$4 Product_3 0 −1.5 25 8 6 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Choose the product Product 1 Product 2 Product 3Four proposals are being considered with investment and NPW shown below. C can only beconsidered if B is implemented. B and D and E are mutually exclusive. The budget is $80.A B C D EInvestment $10 $20 $30 $40 $50NPW $34 $28 $20 $16 $32a) Formulate this as a 0-1 integer program (objective function and constraints).b) Use trial and error to find all feasible solutions, and indicate which is optimal.c) Set up this problem in Excel, and use Solver to find the same optimal solution
- Mr Sng is a retiree in his late sixties. He has $100,000 to invest. He has no regular source of income and no other assets. He is evaluating between 3 different lump-sum financial products shown in Table 3. All products require a minimum investment sum of $100,000. Monetary returns represent the net gain after one year of investing in the product. For example, if Mr Sng chose to invest in Product B, he may lose $5,000 after one year if the GDP growth is negative. He will earn $8,000 if the GDP growth exceeds 2% at the end of the year. If you were in the shoes of Mr Sng, how would you select the appropriate investment product for a time horizon of one year? (i) Use the Optimistic, Conservative and Regrets payoff analysis approaches. State which product(s) Mr Sng should invest in and what monetary return he can expect from each approach (ii) As you have only enough funds for one product, identify the most appropriate investment product. [Hint: Be sure to consider the…Type the linear program, optimal solution, and objective function value in a word document. Submit your excel file. An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income? Investment Expected Return Maximum Allowed Low-income mortgage loans 6.50% 20% Conventional mortgage loans 6.00% 30% Government sponsored mortgage loans 8.25% 25% Bond investments 5.75% 15% Stock investments 8.75% 18% Futures trading 9.25% 10%Variable cells Cell Name Final Value Reduced Cost Objective Coefficient Allowable Increase Allowable Decrease $B$6 Activity 1 3 0 30 23 17 $C$6 Activity 2 6 0 40 50 10 $D$6 Activity 3 0 –7 20 7 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H. Side Allowable Increase Allowable Decrease $E$2 Resource A 20 7.78 20 10 12.5 $E$3 Resource B 30 6 30 50 10 $E$4 Resource C 18 0 40 1E+30 22 What is the optimal objective function value for this problem?
- Problem 2: Comp-Max Computers assembles computers and computer equipment. It is about to start production of threenew types of computers, called model X, Y, and Z, respectively. Each type will require assembly time, inspection time, and storage space. The availability of each of these resources is limited. Specifically, available assembly time is 400 hours, available inspection time is 300 hours, and available storage space is 500 cubic feet (about 14.2 ms). The amount of each resource required for the different products is reported in the table below. Model X earns a profit of $100 per unit, model Yearns a profit of $125 per unit, and model 2 earns a profit of $200 per unit. Due to some prior agreements with customers, Comp-Max must produce at least 12 model X computers. In addition, management requires that the fraction of total production made up of model 2 computers must not exceed 25%. RESOURCE REQUIREMENTS Assembly time Inspection time Storage space MODEL hrs/unit hrsJunit cu.…Based on the following sensitivity report, what would be the impact of changing the objective function coefficient for Product_1 to 17 and changing the objective function coefficient for Product_3 to 10? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 12 7 1E+30 $B$3 Product_2 175 0 8 1E+30 9 $B$4 Product_3 0 −1.5 8 3 1E+30 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Fill the blanks Applying the 100% rule _________________ because the total change in the objective function coefficients ______________ 100%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.