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A meat processor blends four ingredients to produce sausages. Each kilo of this

ID: 409973 • Letter: A

Question

A meat processor blends four ingredients to produce sausages. Each kilo of this sausage is required to have at least 12% protein content, no more than 29% fat content, no more than 85% moisture content, at least 6% spice, and at least 60% meat. Relevant pieces of information about the various ingredients are presented below. Formulate an LP model (objective function & constraints) than can be employed to solve for the optimal ingredient mix. Var, Ingredient Cost Protein Fat Moisture kilo A. Chuck (meat) 37 20 574 B. Beef (meat) 31 17 2062 C. Pork (meat) 16 9 53 37 D. Spice E. 15 100 12 Water Indicate the appropriate coefficients, right-hand side values and signs () for the constraints & objective function of the above problem RHS Min or Max Obj. Func Protein Fat Content Moisture Spice Meat Total Mix

Explanation / Answer

lp formulation is as follows:

Objective function: Min 37A + 31B + 16C + 12D + 0E   (total cost)

Constraints:

.2A + .17B + .09C > .12

.05A + .2B + .53C <= .29

.74A + .62B + .37C + .15D + 1E <= .85

1D >= .06

1A + 1B + 1C >= .60

1A + 1B + 1C + 1D + 1E = 1

A,B,C,D,E >= 0

Min A B C D E RHS Obj. Func. 37 31 16 12 Protein 0.2 0.17 0.09 >= 0.12 Fat Content 0.05 0.2 0.53 <= 0.29 Moisture 0.74 0.62 0.37 0.15 1 <= 0.85 Spice 1 >= 0.06 Meat 1 1 1 >= 0.6 Total Mix 1 1 1 1 1 = 1
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