Question

sarah is trying to decide what combination of cups and plates to buy. her budget is $18. plates cost $6 each and cups cost $3 each. the numbers in the table represent total utility. given her budget, which combination will maximize total utility?

Answer 1

To maximize total utility within a budget of $18, Sarah must find the right combination of $6 plates and $3 cups, though exact figures can't be provided without the utility table. This decision is based on the principle of equalizing marginal utility per dollar spent for both items.

Step-by-step explanation:

Sarah is trying to maximize her total utility within a budget of $18. With plates costing $6 and cups costing $3, she needs to find the combination of these items that will give her the greatest satisfaction. To solve this, we can use the concept of marginal utility per dollar spent, which implies looking at the additional utility gained from spending one more dollar on an item. However, without the actual table of total utility values for each combination of cups and plates, we cannot specify the exact combination. In general, Sarah would need to keep purchasing the item that gives her the highest marginal utility per dollar spent until she reaches her budget limit or until the marginal utility per dollar spent equalizes for both items, which is illustrated by the equation 1.6 = 1.6 within the context of this problem.

Answer 2

Among the given options, the combination that maximizes total utility within Sarah's budget of $18 is "1 plate and 4 cups," with a total utility of 78. Option 3

Combination that maximizes total utility

Let's evaluate the combinations of plates and cups based on Sarah's budget of $18.

Each plate costs $6, and each cup costs $3. Sarah's budget allows for a maximum of 3 plates ($18 / $6 per plate) or 6 cups ($18 / $3 per cup).

Here are the combinations within her budget:

3 plates and 0 cups:

Total cost = 3 plates * $6 = $18

Utility = 70 (utility from plates)

0 utility from cups

Total 70

2 plates and 2 cups:

Total cost = 2 plates * $6 + 2 cups * $3 = $12 + $6 = $18

Utility = 50 (utility from plates) + 23 (utility from cups) = 73

1 plate and 4 cups:

Total cost = 1 plate * $6 + 4 cups * $3 = $6 + $12 = $18

Utility = 26 (utility from plates) + 52 (utility from cups) = 78

0 plates and 6 cups:

Total cost = 6 cups * $3 = $18

Utility = 0 (no utility from plates) + 75 (utility from cups) = 75

Among the given options, the combination that maximizes total utility within Sarah's budget of $18 is "1 plate and 4 cups," with a total utility of 78.

Sarah is trying to decide what combination of cups and plates to buy. Her budget is $18. Plates cost $6 each and cups cost $3 each. The numbers in the table represent total utility. Given her budget, which combination will maximize total utility?

Quantity Plates Utility from Plates Quantity Cups Utility from Cups

1 26 1 10

2 50 2 23

3 70 3 38

4 88 4 52

5 103 5 64

6 115 6 75

Select the correct answer below:

3 plates and 0 cups

2 plates and 2 cups

1 plate and 4 cups

0 plates and 6 cups