Consider a consumer's utility function given by $u(x,y)=2x+y.$ The initial

price of good $x$ is $3$ per unit, the price of good $y$ is $2$ unit, and her income is

$30.$ If the price of good $x$ then increases to $5$ per unit, which one of the

following statements is correct?

a$.$ The consumer decreases her consumption of good $x$ by $5$ units and increases her consumption of good $y$ by $2$ units

b$.$ The consumer decreases her consumption of good $x$ by $10$ units and increases her consumption of good y by $15$ units

c$.$ The consumer decreases her consumption of good $x$ by $5$ units and increases her consumption of good $y$ by $15$ units

d$.$ The utility of the consumer increases because she is consuming less of the more expensive good

e$.$ The consumer's total expenditure on good y is unchanged as its price remains the same

f$.$ The consumer decreases her consumption of good $x$ by $3$ units and increases her consumption of good $y$ by $2$ units

g$.$ The consumer's total expenditure on good $x$ remains unchanged as she only consumes good $y$

h$.$ None of the other statements is correct