Suppose the total utility function for the consumer who is consuming two goods, good x and good z is U(x, z) = ln(2x) + 2lnz.  The consumer’s income is $16 and is faced with the prices of each unit of good x and good z.  The price per unit of good x is $4 and the price per unit of good z is $1.  How many units of good x and good z should the consumer consume so as to maximize his/her utility?  Also, what will be the total utility earned from the consumption of that many units of good x and good z?

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