Question $7(20$ points$)$ PLEASE HELP ME WITH $($C$)$ sketching the graph

Suppose a consumer spends all his income of $$1200$ on the two goods A and $B.$ Good $A$ co $$20$ per unit and good $B$ costs $$30$ per unit. His goal is to consume the combination of goor and $B$ that maximizes his utility. The utility he derives from the consumption of goods $A$ an described by the function $u=4A^{0\mathrm{.}25}{B}^{0\mathrm{.}25}.$

a$.$ Identify the objective function and constraint faced by this consumer.

b$.$ Solve the described constrained optimization problem for A and $B$ using economics concepts.

c$.$ Sketch the solution to this optimization problem $($budget constraint and indifferenc curve$)$ with $A$ on the $x$ axis and $B$ on the $y$ axis. To receive full credit, you must labe all axes intersection points, $(2)$ the optimal A and $B$ from part $b,(3)$ the slope at the optimal A and B$,$ and $(4)$ the utility achieved from the optimal A and B$.$Question $7(20$ points$)$

Suppose a consumer spends all his income of $$1200$ on the two goods A and $B.$ Good $A$ co $$20$ per unit and good $B$ costs $$30$ per unit. His goal is to consume the combination of goor and $B$ that maximizes his utility. The utility he derives from the consumption of goods $A$ an described by the function $u=4A^{0\mathrm{.}25}{B}^{0\mathrm{.}25}.$

a$.$ Identify the objective function and constraint faced by this consumer.

b$.$ Solve the described constrained optimization problem for A and $B$ using economics concepts.

c$.$ Sketch the solution to this optimization problem $($budget constraint and indifferenc curve$)$ with $A$ on the $x$ axis and $B$ on the $y$ axis. To receive full credit, you must labe all axes intersection points, $(2)$ the optimal A and $B$ from part $b,(3)$ the slope at the optimal A and B$,$ and $(4)$ the utility achieved from the optimal A and