A chocolate manufacturer is producing three different types of chocolates: small packages of individually wrapped milk chocolate
Question:
A chocolate manufacturer is producing three different types of chocolates: small packages of individually wrapped milk chocolate squares (for a total of 5.32 ounces), singular 3.5 ounces dark chocolate bars, and white chocolate baking chips in bags of 12 ounces. The maunfacturer has 22000 ounces of sugar, 8000 of milk solids, 4000 of cocoa fat, and 5000 of chocolate liquor. It is your job to determine how much of each ingredient goes into each kind of chocolate item using these resources available. However, you can't have a chocolate bar of pure sugar, of course. Therefore, a table can be found below per US FDA regulations that you'll need to use to place constraints onto each of the products. For example, dark chocolate cannot be called dark chocolate unless it contains at least 35% of chocolate liquor and less than or equal to 12% of milk solids. Please also keep in mind that white chocolate should not contain ANY chocolate liquor at all. Additionally, please make the assumption that an ounce of input ingredients directly equal an ounce of output, so for example, if you mix 2 ounces of sugar and 2 ounces of cocoa fat, you have 4 ounces to create any of these chocolate products. Complete the model by maximizing the revenue for the business while meeting all other constraints. Use a linear program to solve the model - using only Simplex LP. Do not use an integer constraint as the manufacturer will be ok if decimal numbers are present in the model.
| Milk | Dark | White |
| Ounces per package, bar, or bag | ||
| 5.32 | 3.5 | 12 |
| Selling price (per package, bar, or bag) | ||
| $3.25 | $2.25 | $8.00 |
| Chocolate | Chocolate Liquor | Milk Solids | Sugar | Cocoa Fat |
| Milk | ≥ 10% | ≥ 12% | ||
| Dark | ≥ 35% | ≤ 12% | ||
| White | ≥ 14% | ≤ 55% | ≥ 20% |
Expert Answer:
