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Linear Programming: 4. Kings Department Store has 625 nubies, 800 diamonds, and 700 emeraids from which they will make bracelets and necklaces that they have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds Kings will net a profit of S250 on each bracelet, which is made with 2 nubies, 3 diamonds, and 4 emeralds, and $500 on each necklace, which includes 5 rubies, 7 diamonds, and 3 emeralds. Formulate as an LP problem to maximize profit? Formulate the above problem as a Linear Programming Model. a (5 points) b. Graphically solve the Linear Programming Model (solve it using the "comer point method) (20 points) Linear Programming 5) Louis Payton Company produces two basic types of plastic pipe. Three resources are crucial to the production: extrusion hours, packaging hours, and a special additive to the plastic raw material. The following data represent next week's situation. Resource availability Resource requirements. per unit of type 2 6 hrs Resource requirements per unit of type 1 4 hrs 2 hrs Resource 48 hrs 18 hrs 16 lbs Extrusion Packaging Additive mix 2 hrs 1 lb 2 lbs The profit per unit is $34 for type 1 and $40 for type 2. The company wants to determine how much of each type of pipe should be produced to maximize the total profits. The formulation for the above Linear Program is shown below. 2,Nurber f TYPE 1 Plashe Pp to d Maximi2e heutve 2- 3421+40 Naits S 48 hons S18 Lous 16 ILS 632 Estusin 431 t 22 2 t 22 WILEY Citeseds 1302 taly 198 indad The Lincar Program from (above) is solved uning MS-Excel. Refer so tbe enclosed "Ansuar 30d Sensitivity reports below and answer the below questions (Hint All questions below can be answered from the Answer and Semsitivity reports. Do sot waste time in solving for new Linear Programs to obtain Answers) a) Which decision variables are basic, and which decision variables are non-basic? Which constraints anre binding, which coestraints are non-binding? What is the optimal solution and what is the total peofic b) How mch would the total profits increase if the profit per unit of type 1 pipe i increased to $422 How mach would the total profits increase if the profit per unit da type 2 pipe is increased to $427 c) How much would the total profits increase if the profit per unit of type 1 pipe is decreased to 530? How much would the total profits increase if the profit per unit of type 2 pipe is decreased to $30? d) If the company has three options: first, increasing the extrusion hours availability by 5 hours at the cost of S5 per hour, second, increasing the packaging hours availability by 1 hour at the cost of $6 per hour; and third, increasing the additive mix by 2 lbs at the cost of $2 per lb. Which option should the company choose? Explais. c). Based on the option chosen in part d), how much more profits would the company make after deducting the cost? (20 points) Answer report Target Cell (Max) Final Value Original Value Cell Name 342 SDS3 Total profits Adjustable Cells Final Value 3 Original Value Cel Name $B$3 Amount to be produced Type1 SC$3 Amount to be produced Type 2 0 Constraints Slack Status Formula 48 SD55-SES5 Binding 18 SD$6cSES6 Binding 12 SD$7SE$7 Not Binding Cell Value Name Cell $D$5 Extrusion hrs SD$6 Packaging hrs SD$7 Additive mix 0 4 US tnests wes itedde leame. be Cast SagLga re d 2 Dathides wnhates les t Sensitivity report Adjustable Cells Final Reduced Objective Alowable Allowable Cell Name $853 Amount to be produced Typet SC$3 Amount to be produced Type 2 Coefticient Increase 34 40 Decrease 7.3333333339 11 Value Cost C Constraints Final Shadow Constraint Allowable Allowable Name Value Price R.H. Side 3 Increase Decrease Cell 48 $D$5 Extrusion hrs SDS6 Packaging hrs 48 18 2 18 11 C 1E+30 12 16 SD$7 Additive mix

Answer 1

the rounded off solution is to make 132 bracelets and 58 necklaces

however, this solution uses 802 diamonds and 702 emeralds and is infeasible

so we round down solution as 131 bracelets and 57 necklaces

the solution is feasible but gives a profit of

$61250

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