Linear Programming 2 Formulation 2 Maximization LPP
#Operations Research
#OR
#Linear Progremming
#Formulation
OR, Operations Management, Math, Statistics, OM, Operations Management, Programming, Formulation, Maximization, Minimization, Decision Variables, Objective Function, Constraints, LPP, MBA, MCA, CA, CS, CWA, BBA BCA, BCom, MCom, GRE, GMAT, Grade 11, Grade 12, Class 11, Class 12, IAS, CAIIB, FIII, IBPS, BANK PO, UPSC, CPA, CMA
We can list the following important point when we are to formulate any managerial or real life problem:
The steps to model a problem are the following:
Step 1: Determining decision variables and expressing them algebraically. X1,..., Xn
Step 2: Determining Objective Function.
Maximize or minimize Z = C1•X1 + C2•X2 + ... + Cn•Xn
Step 3: Determining the restrictions and expressing them as equations or inequalities in function of the decision variables:
A11•X1 + A12•2 + ... + A1n•Xn (≥, ≤, or =) b1
A21•X1 + A22•X2 + ... + A2n•Xn (≥, ≤, or =) b2
...
Am1•X1 + Am2•X2 + ... + Amn•Xn (≥, ≤, or =) bm
Step 4: Expressing all implicit conditions established by the origin of variables: negativeness, integer, only a few allowed values, ...
X1,..., Xn ≥ 0
X1,..., Xn are integers,
Raja Toys Mfg Ltd manufactures wooden soldiers and trains. Each soldier sells for Rs. 27, uses Rs. 10 of raw materials and takes Rs. 14 of labor & overhead costs. Each train sells for Rs. 21, uses Rs. 9 of raw materials, and takes Rs. 10 of overhead costs.
Each soldier needs 2 hours finishing and 1 hour carpentry; each train needs 1 hour finishing and 1 hour carpentry. Raw materials are unlimited, but only 100 hours of finishing and 80 hours of carpentry are available each week. Demand for trains is unlimited; but at the most 40 soldiers can be sold each week.
How many of each toy should be made each week to maximize profits? Formulate this as an LPP.
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