| Your company manufactures TVs, stereos and speakers, using a common parts inventory | |||||||||
| of power supplies, speaker cones, etc. Parts are in limited supply and you must determine | |||||||||
| the most profitable mix of products to build. | |||||||||
| TV set | Stereo | Speaker | |||||||
| Number to Build-> | 0 | 0 | 0 | ||||||
| Part Name | Inventory | No. Used | |||||||
| Chassis | 450 | 0 | 1 | 1 | 0 | ||||
| Picture Tube | 250 | 0 | 1 | 0 | 0 | ||||
| Speaker Cone | 800 | 0 | 2 | 2 | 1 | ||||
| Power Supply | 450 | 0 | 1 | 1 | 0 | ||||
| Electronics | 600 | 0 | 2 | 1 | 1 | ||||
| Profits: | |||||||||
| By Product | $0 | $0 | $0 | ||||||
| Total | $0 | ||||||||
| Problem | |||||||||
| Your company builds TVs, stereos and speakers, using a common parts inventory of power supplies, | |||||||||
| speaker cones, etc. Parts are in limited supply. What is the best combination of products to build | |||||||||
| that maximizes profit? | |||||||||
| Solution | |||||||||
| 1) The variables are clearly the number of TVs, stereos and speakers to build. In this worksheet, they | |||||||||
| are given the name Number_to_build. | |||||||||
| 2) The constraints specify that the number of parts used cannot exceed the supply. This leads to | |||||||||
| Number_used <= Number_available | |||||||||
| There is also the logical constraint | |||||||||
| Number_to_build >= 0 via the Assume Non-Negative option | |||||||||
| 3) The objective is to maximize profit. In the ProductMix worksheet this is defined as Total_profit. | |||||||||
| Remarks | |||||||||
| Although this is a good example of a product mix problem, bear in mind the limitations of the | |||||||||
| model. For example, market demand and price elasticity is not included in the model -- we assume | |||||||||
| that it doesn't matter how many TVs we build, we will always be able to sell them. Nor are there any | |||||||||
| pre-specified minimum or maximum of products that need to be made. The effect of introducing | |||||||||
| these restrictions can be studied by examining a Sensitivity Report, which you can select from the | |||||||||
| dialog appears with the message 'Solver found a solution.' | |||||||||
