Inorder to create the model for this situation, I first need to identify thegoal, decision variables, and production restraints. The goal is toidentify the optimal capacity utilization for the various product groups, inorder to maximize our profit. Our decision variables, which weadjust in order to achieve our goal, are the number of each product that weproduce. As for restraints, we have 2 categories, Capacity restraints &Demand restraints. Our capacity Restraints relate to our ability to perform a maximumnumber of repetitions of the various steps in the process. In this example,there are 4 steps, and we are able to perform each step a maximum number oftime in any month, as follows:Capacity Restraints· Printing:A maximum of 1,600 hours of printing is possible each month.· Mounting:A maximum of 2,600 hours of mounting is possible each month.· Assembly:A maximum of 1,700 hours of assembly is possible each month.
· Inspection:A maximum of 1,500 hours of inspection is possible each month.Our demand restraints relate to customer demand for the products. If weare producing more products than there is demand for, we will be losing moneyon each product we make beyond demand. Thus we want to restrict our productionnumbers to below the following demand restraints provided.Demand Restraints· HyperLink:A maximum of 210 each month.· FastLink:A maximum of 370 each month.· SpeedLink:A maximum of 450 each month.
· MicroLink:A maximum of 180 each month. B. Thisapproach is not very effective without further analysis, because it does nottake into account the resources required to produce these high margin products.
Though it is true that our margins are higher per product on FL & HL, if weare only able to produce a small number of these products due to heavy productionrequirements, our overall profit may be smaller than if we produce a very largenumber of products that have a smaller profit margin. C. Myalgebraic model formulation is as follows:Printing Capacity: 1ML + 1.5SL + 1.5FL + 0.5HL =< 1600MountingCapacity: 1.5ML + 3SL + 4FL + 5HL =< 2600AssemblyCapacity: 2ML + 1SL + 3FL + 4HL =< 1700InspectionCapacity: 0.
5ML + 0.5SL + 1FL + 0.5HL =< 1500 ML =<180SL =<450FL =<370HL =<210Figure 1 shows Excel Solver with restriction formulasinput into the Solver parameters.
Accordingto my report, the optimal number of each product to produce is as follows:· HyperLink:0· FastLink:245· SpeedLink:450· MicroLink:180 D. Idon’t think that the result is intuitive. It is not intuitive to avoid producingthe product that provides the highest profit margin. To explain the result inan intuitive rule, I would say, “Prioritize the products that best maximizeyour resource limitations. By better utilizing your resources, you are able to increasethe number of products you can sell to create profit.
E. Yes Ithink it is still valid. As my resource decreased (number of printing hours Ihave), the number of HyperLink’s increase, as it is best able to utilize thisresource.
The SpeedLink & FastLinks, require the most of this resource, andwe see a reduction in FastLinks as a result. We can justify keeping Speedlinksat their current level because they better utilize the other resourcescomparable to FastLinks.Figure 2 shows that as my printing resource decreases,my Hyperlink production increases as it most efficiently utilizes thedecreasing resource. Production of Fastlinks, which are less efficient with theresource, decreases.F. Basedon our model and existing “rule” we have created, I do not believe minorfluctuation in pricing will change our production strategy. In order to testthis, I have ran the model again reducing the profit margin of our highproduction items (effectively increasing price) and increasing the contributionon our low production items (effectively decreasing price), and I received thesame production recommendations from solver.
Figure 3G. Whenmounting capacity is at 200, a sensitivity report will show us our “shadowprice” of $66.66. This tells us that each additional unit of this resource (onehour of mounting), will increase our maximum objective value by $66.66, butonly up to 70 additional units. Figure 4After 70 hours, we canassume the shadow price will decrease (as scarcity decreases), and we will seea change in the slope of our curve.
Looking at the graphical representation ofthe data, we do in fact notice the shifts in the slope of our chart (Fig. 5). Figure 5 Figure6 Finally, after 3,000hours of mounting, we see our line ‘flat-line”, and not grow in value. Thisimplies that we have maximized another resource, and are unable to produceadditional output, regardless of how much further we increase our Mountingvariable.
Figure 7 illustratesthat at 3,000 mounting hours, we have exhausted our assembly hours. Regardlessof any increases to mounting, we are no longer able to increase our profits, aswe don’t have any mounting hours available. H. Belowis the Screenshot of my Sensitivity Output. It does correspond with theinformation in the previous question.
At 2600 mounting hours, each hour has ashadow price of $40, with an allowable increase of 206.67. This means I canexpect my slope to be the same at 2800 (which is an increase of 200 hours), butthere will be some change at 3,000 hours, because it exceeds the allowableincrease limit, and the value of each hour will change. I. Ibelieve that the minimum profit contribution should be greater than $40/hour tobe financially attractive. Our sensitivity report indicates that we are able toreduce our operations mounting input by 980 hours and maintain our currentvalue. Because the 300 hours is within this allowable range, we can calculatethe value of each hour to be worth at least $40. The answer does not changebased on the price of existing mounting equipment, because this is a sunken costthat is placed into the fixed cost area, and does not influence my contributions.
Appendix(A) The belowimage shows my solver parameters, which identifies my Goal, Lists all 8 of myconstraints, and identifies my decision variables.