The decision maker wishes to maximize the total benefit associated with three ac
ID: 1099410 • Letter: T
Question
The decision maker wishes to maximize the total benefit associated with three activities X, Y, and Z. The price per unit of activities, X, Y, and Z is $1, $2, and $3 respectively. The following table gives the ratio of the marginal benefit to the price of the activities for various levels of each activity:
Level of activity
MBx
Px
MBy
Py
MBz
Pz
1
10
22
14
2
9
18
12
3
8
12
10
4
7
10
9
5
6
6
8
6
5
4
6
7
4
2
4
8
3
1
2
a. If the decision maker chooses to use one unit of X, on unit of Y, and one unit of Z, the toatal benefit that results is $____________
b. For the fourth unit of activity Y, each dollar spent increases total benefit by $___________ The fourth unit of activity Y increases total benefit by $____________
c. Suppose the decision maker can spend a total of only $18 on the three activities. What is the optimal level of X, Y, and Z? Why is this combination optimal? Why is the combination 2X, 2Y, and 4Z not optimal?
d. Now suppose combination the decision maker has $33 to spend on the three activities. If the decision maker has $35 to spend, what is the optimal combination? Explain.
Level of activity
MBx
Px
MBy
Py
MBz
Pz
1
10
22
14
2
9
18
12
3
8
12
10
4
7
10
9
5
6
6
8
6
5
4
6
7
4
2
4
8
3
1
2
Explanation / Answer
b) 1st blank = 9/3 = 3, 2nd blank = 9
c) activity 1. He will spent entirely on y so benefit = 18 * 22 = 396
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