Need help

if bridget has wine and cheese. 4 bottle of wine at 10.00 and 4lbs of chesse 4.00. The last bottle of wine added 50 units to bridgt utility, while the last pound of cheese added 40 units.
Is bridget makeing the utility maximaizing choice if so why if not why.
My answer
No
if u= f (x,y0
50=(10,4)+ (10,4)
2000 + 1600
I am stuck or am i going in the right direction

No, you are way off track. For utility maximization in spending on goods, you want the spend where the marginal utility per dollar is the highest. So, if MUx/Px is greater than MUy/Py then spend more on x and perhaps less on y.

I presume your "10.00" is the price per bottle of wine rather than the price for the 4 bottles. Ditto for the cheese.

So MU/P of wine is 50/10 = 5. MU/P of cheese is 40/4=10. Bridget should buy more cheese and less wine.

It seems like you are on the right track, but let's go through the steps together to find the answer.

In order to determine if Bridget is making the utility-maximizing choice, we need to calculate the marginal utility per dollar for both wine and cheese.

First, let's calculate the total utility for the wine and cheese separately. We know that the last bottle of wine added 50 units to Bridget's utility, and the last pound of cheese added 40 units.

For the wine:
Total utility for the 4 bottles of wine = 4 (number of bottles) * 50 (units added per bottle) = 200

For the cheese:
Total utility for the 4 pounds of cheese = 4 (number of pounds) * 40 (units added per pound) = 160

Next, we need to calculate the total cost of the wine and cheese. We know that each bottle of wine costs $10 and each pound of cheese costs $4.

Total cost of wine = 4 (number of bottles) * $10 (cost per bottle) = $40
Total cost of cheese = 4 (number of pounds) * $4 (cost per pound) = $16

Now, let's calculate the marginal utility per dollar for both wine and cheese.

Marginal utility per dollar for wine = Total utility for wine / Total cost of wine = 200 / 40 = 5
Marginal utility per dollar for cheese = Total utility for cheese / Total cost of cheese = 160 / 16 = 10

Finally, to determine if Bridget is making the utility-maximizing choice, we compare the marginal utility per dollar for both wine and cheese.

In this case, the marginal utility per dollar for cheese (10) is greater than the marginal utility per dollar for wine (5).

Since Bridget obtains more utility per dollar from consuming cheese, she should consume more cheese and less wine in order to maximize her utility.

Therefore, Bridget is NOT making the utility-maximizing choice in this scenario. She should allocate her resources differently to maximize her overall satisfaction.