Linear Programming, Quantative
Okay, this is an example problem that my teacher gave me to figure out, if I can figure out how to do this, then I will be ok for my upcoming quiz.
I use management scientist so I just need to be able to come up with the constraints and the variable coefficients and then I can just enter them and solve. The question is, how do I come up with the information? Could someone guide me through it? Thanks
FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below.
Ingredient Cost/ Volume/ Fat Grams/ Calories
Dried Fruit .35/ .25 cup/ 0/ 150
Nut Mix .50/ .375 cup/ 10/ 400
Cereal Mix .20/ 1 cup/ 1/ 50
The company needs to develop a linear programming model whose solution would tell them how many ounces of each mix to put into the TrailTime blend. TrailTime is packaged in boxes that will hold between three and four cups. The blend should contain no more than 1000 calories and no more than 25 grams of fat. Dried fruit must be at least 20% of the volume of the mixture*, and nuts must be no more than 15% of the weight of the mixture**.
Develop a model that meets these restrictions and minimizes the cost of the blend, using MS, Excel Solver, or an online LP solver. What is the optimal solution? (that is, how much does a box cost, and how many ounces of each ingredient does it contain?)
(*hint: develop an expression for the total volume of the mixture, and an expression for the volume of the dried fruit. Then create an inequality that states that the dried fruit volume must be at least 20% of the total volume; then re-arrange this inequality so that all expressions containing variables are on the left-hand side. Create constraints for calories, fat, and weight in similar fashion)
(** this is simpler, since each mixture has the same weight, one ounce)