In response to your report and request regarding Merton’s financial performance and product mix, I have met with your controller, sales manager and production manager, and have provided a solution that will improve the company in these two areas. Using a systematic approach, I was able to analyze the current machine hours, standard costs, and overhead budget. My findings have allowed me to determine the best monthly product mix that will maximize Merton’s total monthly contribution.
Furthermore, I have addressed the decision regarding outsourcing, and have provided both the maximum rent your company should pay in addition to the maximum number of hours that should be rented. When determining the product mix, I took careful consideration of the machine hour constraints that your factory must account for. The following sections will provide further information in regards to my analytical technique, and how I was able to determine these figures. Current Situation Merton’s third and fourth quarters of last year should not be deemed a failure, but rather an area where the company can improve.
It is evident your company’s current product mix is not meeting the financial standards that the company expects. As your sales manager pointed out, Model 101 trucks currently cost $40,205 to produce and are selling at a price of $39,000, meaning the company is producing this model at a loss. Some other issues to point out are the current capacity levels. Although the company is profiting on each Model 102 sold, maxing out capacity for this model may not be the best solution, as suggested by the controller.
An analysis of the provided budget will allow us to track where the company’s money is being spent, and will suggest certain areas where possible changes can be made. Evaluating the different scenarios will answer our current questions on whether to stop producing Model 101’s all together, to continue producing both models but at different amounts, and/or to consider the use of an outside supplier. Data Used in the Analysis To address the main goal of increasing financial performance, I had to define the objective of the current situation.
Simply put, the objective is to maximize total contribution from the two models, which will directly improve Merton’s financial performance. Our focus is contribution rather than profit because contribution deals only with variables costs and variable costs are costs that we can manipulate to better Merton’s financial position. By determining exactly how much contribution Merton receives from producing one Model 101 and one Model 102, we can attempt to maximize these figures. A product’s contribution is the amount of money the company receives after subtracting out the variable production costs.
Figure 1 shows the contribution received for producing one truck of Models 101 and 102. I was able to calculate this figure using the data provided from Tables B and C in your report. Table B listed the variable costs which include the direct materials and direct labor costs per model. I then added the variable overhead costs per unit that were listed in Table C. Subtracting these variable costs from the total selling price leaves us with Model 101 attributing $3,000 in contribution and Model 102 attributing $5,000. The second goal is to determine an optimal product mix.
In order to do so, I had to account for any constraints, or parameters that limit production and affect total monthly contribution. Table A from your report provided these constraints, which are the production capacities of the four departments, engine assembly, metal stamping, Model 101 assembly and Model 102 assembly. These constraints, which will be
Decision variables help us do exactly that, make decisions. Since product mix is the decision we are making, the decision variables represent the number of 101 and 102 units that Merton should produce each month. These variables are represented as X101 and X102. Having identified our variables I was now able to setup a mathematical equation that will calculate Merton’s maximum contribution per month. The equation is as follow: Maximum Contribution = $3,000*X101 + $5000*X102 Method of Analysis: Linear Programming
After reading the report and understanding the variables involved, I realized that linear programming would be a useful tool in this situation. Linear programming (LP) is beneficial because it assists in decision making when resource allocation is involved. Our situation calls for a better approach when allocating labor, machinery, money, time and materials, thus making LP the perfect fit. For this situation, linear programming is more than an option. It is a must. Due to our number of constraints, using a linear program will compute exact outputs that will save time and eliminate the risk of human error.
The program will allow us to input the known variables (101 and 102 contribution), and will calculate the optimal product mix, while staying within the parameters of our listed constraints (Figure 2). Analyzing the Options with Solver Optimal Product Mix Now that you have an understanding of the capabilities of linear programming, I will explain how I was able to use this model when persuading your sales manager, controller and production manager. Although these three do not agree on how Merton is currently allocating its resources, one aspect where they do agree is that maximizing contribution is Merton’s main focus.
After explaining that this linear program, known as “Solver,” can calculate optimal product mix on the basis of maximum contribution, I received their undivided attention. Solver’s product mix calculation stated that Merton Truck Co. should produce 2,000 Model 101 trucks and 1,000 Model 102 trucks each month. Using this product mix will provide a maximum contribution of $11,000,000 per month. The objective formula that was presented above shows this calculation: $3,000*(2,000101)+5000*(1,000102)= $11,000,000 total contribution per month.
Remember, this formula is calculated while staying within each of Merton’s production constraints. Simply producing more or less of either model will do one of two things. One, it would exceed one of our given constraints, or two, it would produce a total contribution that is lower than $11 million. Solver’s suggestion to produce 2,000 Model 101’s proves that the controller was correct in his objection of the sales manager. The model confirms that doubling Model 101 production allows the fixed overhead of 2. 7 million to be absorbed over 2,000 models instead of 1,000 as the company is currently doing.
Since Merton pays fixed overhead of 2. 7M. for 101’s and only 1. 5M for 102’s, it makes sense to “get your money’s worth” by producing more 101’s. Renting Additional Capacity In addition to providing the optimal product mix, Solver has a number of other capabilities that help support my recommendations. One capability is that Solver can help us determine whether the production manager was correct when suggesting to rent additional capacity from an outside supplier. After the variables are input into the Solver program, I run the calculation.
Once the program has calculated the data, it provides us with a “sensitivity report” that focuses on our available resources (constraints) and tests a number of “what-if scenarios. ” For this situation, it will help us determine the amount to pay per rented hour and exactly how many additional hours to rent. Two relevant categories to note from the sensitivity report are the “shadow price” and the “allowable increase”. The program provides a shadow price which states that for each additional unit produced, Merton will receive ‘X’ dollars in contribution. The shadow price for engine assembly was $2,000.
Therefore, for each additional unit of capacity (rented hours), Merton can afford to pay a maximum of $2,000. In regards to the allowable increase, Solver suggests that Merton should purchase a maximum of 500 rented hours. After 500 hours have been purchased, there is no further increase in contribution. The use of Solver has once again proven beneficial. Although the production manager’s suggestion was correct, Solver has strengthened his argument by providing objective data that tells us a max price to pay in addition to the maximum number of hours to rent.
Additional Constraint – Producing at a 3:1? After finding out from the optimal product mix that it is more beneficial to produce two times the number of Model 101’s than Model 102’s, why not increase production to three to one? We can test this proposal by simply adding an additional constraint to our linear program. As expected, the optimal product mix was forced to change to a 3:1 ratio. Adhering to this constraint provided a product mix of 2,250 Model 101’s and 750 Model 102’s. However, the unwanted consequence is noticed in total monthly contribution.
Plugging this product mix into our objective equation shows that contribution actually decreases. $3,000*(2,250101)+$5000*(750102) = $10,500,000. Seeing this drop in monthly contribution further proves that our previous optimal product mix of a 2:1 ratio should remain in place. Closing As mentioned in the previous sections, linear programming is a useful technique that should be applied to help improve Merton’s financial performance. My recommendation is that the company immediately implements a product mix of 2,000 Model 101 trucks and 1,000 Model 102’s.
Secondly, the company should rent additional capacity from an outside supplier. However, your company must not pay more than $2,000 per hour, and not rent more than 500 hours because this would no longer increase total contribution. Although linear programming is widely used and often very accurate, no model is perfect. One disadvantage of linear programming is that it does not take into account industry trends. Choosing to produce two times the amount of Model 101’s does not guarantee this model will sell two times as much. Furthermore, linear programming is only useful in solving linear scenarios.
Real world constraints are not always linear. For instance, a constraint that involves “number of staff members required per model” would be impossible to calculate when the other constraints are based on hours. Additionally, linear programming does not account for risk. What if the supplier cannot provide materials for one month’s time? What if Model 101 is using defective parts and the line becomes halted? These are items to consider when implementing LP, but by no means should they prevent Merton Trucks from implementing the model. Figure 1: Contribution per Model Model 101|
Sell Price| $39,000| Direct Materials| $24,000| Direct Labor| $4,000| Variable Overhead| * $8,000| Contribution| $3,000| Model 102| Sell Price| $38,000| Direct Materials| $20,000| Direct Labor| $4,500| Variable Overhead| * $8,500| Contribution| $5,000| Figure 2: Constraints Machine-Hours: Requirements and Availability| Department| Required Machine Hrs. Model 101 Model 102| | Total Machine Hrs. Available per Month| Engine Assembly| 1| 2| <=| 4,000| Metal Stamping| 2| 2| <=| 6,000| Model 101 Assembly| 2| -| <=| 5,000| Model 102 Assembly| -| 3| <=| 4,500|