Determine the amount of composite commodities, Microeconomics

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a) Joan's utility function can roughly be estimated as :

U = 60Q₁^3/4Q₂^2/3

She chooses from two composite commodities Q₁ and Q₂ whose prices per unit are kshs 20 and Kshs 15 respectively. He has Kshs 6000 to spend on the two commodities. Determine the amount of each commodity that he should buy so as to maximize her utility.

b) Joan would like to minimise her expenditure subject to her enjoying 480 utils of utility. Determine the amount of Q₁ and Q₂ she should buy so as to achieve her objective.

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