Consider a consumer who can consume either A or B, with the quantities being denoted by $a$ and $b$ respectively. If the utility function of the consumer is given by $$-[(10-a)^2+(10-b)^2]$$(suppose prices of both goods are equal to $1$), then solve for optimal consumption of the consumer when his income is $40$.

My approach: I have the problem: $$max(-[(10-a)^2+(10-b)^2])$$ $$s.t.\ a+b \le 40,\ a\ge 0,\ b\ge 0.$$ Looking at the objective function, we see that it's maximum value is $0$ when $a=b=10$.

Am I right here?

Question

Consider a consumer who can consume either A or B, with the quantities being denoted by $a$ and $b$ respectively. If the utility function of the consumer is given by $$-[(10-a)^2+(10-b)^2]$$(suppose prices of both goods are equal to $1$), then solve for optimal consumption of the consumer when his income is $40$.

My approach: I have the problem: $$max(-[(10-a)^2+(10-b)^2])$$ $$s.t.\ a+b \le 40,\ a\ge 0,\  b\ge 0.$$ Looking at the objective function, we see that it's maximum value is $0$ when $a=b=10$.

Am I right here?