A food factory makes three types of cereals, A, B and C, from a mix of several ingredients:Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 2kg boxes. Thefollowing table provides details of the sales price per box of cereals and the productioncost per ton (1000 kg) of cereals respectively.Sales price per box($) | Production cost per tonCereal A2.504.00Cereal BCereal C2.002.803.503.00.The following table provides the purchase price per ton of ingredients and the maximumavailability of the ingredients in tons respectively.|Ingredients Purchase price ($) per ton Maximum availability in tonsOates10010ApricotsCoconuts12080Hazelnuts2002The minimum daily demand (in boxes) for each cereal and the proportion of the Oates,Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table,Proportion ofMinimum demand (boxes) Oates | Apricots | Coconuts | Hazelnuts0.05Cereal A10000.80.10.05Cereal BCereal C7000.650.20.050.17500.50.10.10.3a) Let ri; 20 be a decision variable that denotes the number of kg of ingredient i, wherei could be Oates, Apricots, Coconuts, Hazelmuts, used to produce Cereal j, here j isone of A,B,C, (in boxes). Formulate an LP model to determine the optimal productionmix of cereals and the associated amounts of ingredients that maximises the profit, whilesatisfying the constraints.

Given : Types of Cereals, The ingredients are: Demand:

Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates | Apricots | Coconuts | Hazelnuts 0.1 Cereal A 1000 0.8 0.05 0.05 Cereal B 700 0.65 0.2 0.05 0.1 Cereal C 750 0.5 0.1 0.1 0.3 a) Let rij 20 be a decision variable that denotes the number of kg of ingredient i, where i could be Oates, Apricots, Coconuts, Hazelnuts, used to produce Cereal j, here j is one of A,B,C, (in boxes). Formulate an LP model to determine the optimal production mix of cereals and the associated amounts of ingredients that maximises the profit, while

Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates | Apricots | Coconuts | Hazelnuts 0.1 Cereal A 1000 0.8 0.05 0.05 Cereal B 700 0.65 0.2 0.05 0.1 Cereal C 750 0.5 0.1 0.1 0.3 a) Let rij 20 be a decision variable that denotes the number of kg of ingredient i, where i could be Oates, Apricots, Coconuts, Hazelnuts, used to produce Cereal j, here j is one of A,B,C, (in boxes). Formulate an LP model to determine the optimal production mix of cereals and the associated amounts of ingredients that maximises the profit, while

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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