Consider the Following Problem: Maximize Z = 2x₁ + 4x₂

question 4

Essay

Consider the following problem: Maximize Z = 2x₁ + 4x₂ - x₃,subject to 3x₂ - x₃ ≤ 30 (resource 1)2x₁ - x₂ + x₃ ≤ 10 (resource 2)4x₁ +2x₂ - 2x₃ ≤ 40 (resource 3)and x₁ ≥ 0,x₂ ≥ 0,x₃ ≥ 0.(a)Work through the simplex method step by step to solve the problem.(b)Identify the shadow prices for the three resources and describe their significance.

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Definitions:

Moral Hazard

A situation where one party is more likely to take risks because another party bears the cost of those risks, often seen in insurance and financial sectors.

Federal Deposit

Funds deposited in a federal bank or a financial institution that is guaranteed by a government agency.

Insurance Program

A system of protection against financial loss in which risks are pooled and financial compensation is provided to members facing losses.

Congestion Pricing

A pricing strategy that charges users fees for accessing certain areas during peak times to reduce traffic congestion.