why is there no inclusion of the parameter z in the solutions and the budget constraint?

can you please provide a explanation with any mathematical working out

Lucas has $40 per week that he can spend on lemon soda (X) and chips (Y). The price of the lemon soda (PX) is $2 per bottle, and the price of the chips (PY) is $4 price  Write down Lucas’s budget constraint. Draw the budget constraint on the graph below. Make sure to indicate the intercepts and the slope of budget constraint. Label it as BC1.    Provide an economic interpretation of the slope of the budget constraint BC1 Suppose Lucas’s income decreases to $12 per week, and the price of lemon soda and chips remain the same. Write down Lucas’s new budget constraint. Then draw his new budget constraint on the same graph above.  Make sure to indicate the intercepts and the slope. Label it as BC2.    Suppose Lucas’s income remains to be $40 per week and the price of chips remains the same, but the price of lemon soda (PX) increases to $5. Write down Lucas’s new budget constraint. Then draw his new budget constraint on the same graph above. Make sure to indicate the intercepts and the…

Which of the following conditions should hold for an interior optimum? Px MRSXY and PxX + PyY < I Py MUx and MUy should be maximized and Px X + PyY = I Px MRSXY and PxX + PyY = 1 Py MRSXY should be maximized and PxX + PyY = I