To find Mama Mboga's additional satisfaction from consuming an extra piece of Nyama in a day, we need to calculate the change in satisfaction when the quantity of Nyama increases by one.

The satisfaction function is given by S = 2W^2 + 3N^3, where W represents the quantity of Sukuma Wiki and N represents the quantity of Nyama.

We know that Mama Mboga earns an income of 24 Kenya Shillings in a day, and she spends all her income on Sukuma Wiki and Nyama. The price of Sukuma Wiki is 2 shillings and the price of Nyama is 3 shillings.

Let's assume Mama Mboga initially spends her entire income on Sukuma Wiki and Nyama, so W = 12 (since 2 shillings can buy 12 units of Sukuma Wiki) and N = 8 (since 3 shillings can buy 8 units of Nyama).

Now, let's calculate her initial satisfaction using the satisfaction function:
S = 2(12^2) + 3(8^3)
S = 2(144) + 3(512)
S = 288 + 1536
S = 1824

To find the additional satisfaction from consuming an extra piece of Nyama, we need to calculate the new satisfaction when N increases by one. Let's assume Mama Mboga now buys 9 units of Nyama.

Using the satisfaction function:
S' = 2(12^2) + 3(9^3)
S' = 2(144) + 3(729)
S' = 288 + 2187
S' = 2475

The additional satisfaction from consuming an extra piece of Nyama is the difference between the new satisfaction (S') and the initial satisfaction (S):
Additional satisfaction = S' - S
Additional satisfaction = 2475 - 1824
Additional satisfaction = 651

Therefore, the additional satisfaction from consuming an extra piece of Nyama in a day is 651.

Question

To find Mama Mboga's additional satisfaction from consuming an extra piece of Nyama in a day, we need to calculate the change in satisfaction when the quantity of Nyama increases by one.

The satisfaction function is given by S = 2W^2 + 3N^3, where W represents the quantity of Sukuma Wiki and N represents the quantity of Nyama.

We know that Mama Mboga earns an income of 24 Kenya Shillings in a day, and she spends all her income on Sukuma Wiki and Nyama. The price of Sukuma Wiki is 2 shillings and the price of Nyama is 3 shillings.

Let's assume Mama Mboga initially spends her entire income on Sukuma Wiki and Nyama, so W = 12 (since 2 shillings can buy 12 units of Sukuma Wiki) and N = 8 (since 3 shillings can buy 8 units of Nyama).

Now, let's calculate her initial satisfaction using the satisfaction function:
S = 2(12^2) + 3(8^3)
S = 2(144) + 3(512)
S = 288 + 1536
S = 1824

To find the additional satisfaction from consuming an extra piece of Nyama, we need to calculate the new satisfaction when N increases by one. Let's assume Mama Mboga now buys 9 units of Nyama.

Using the satisfaction function:
S' = 2(12^2) + 3(9^3)
S' = 2(144) + 3(729)
S' = 288 + 2187
S' = 2475

The additional satisfaction from consuming an extra piece of Nyama is the difference between the new satisfaction (S') and the initial satisfaction (S):
Additional satisfaction = S' - S
Additional satisfaction = 2475 - 1824
Additional satisfaction = 651

Therefore, the additional satisfaction from consuming an extra piece of Nyama in a day is 651.

Knowee AI · Accepted Answer