Question

An international organization must decide how to spend the $1,800,000 they have been allotted for famine relief in a remote area. They expect to divide the money between buying rice at $38.50/sack and beans at $35/sack. The number, P, of people who would be fed if they buy x sacks of rice and y sacks of beans is given by xy P= 1.1x+y- 108 What is the maximum number of people that can be fed, and how should the organization allocate its money? Round your answers to the nearest integer. Pmax = is attained on buying sacks of rice and sacks of beans.

Answer 1

The maximum number of people that can be fed is approximately 48,140. The organization should allocate its money to buy 1 sack of rice and 48,140 sacks of beans.

Step-by-step explanation:

To determine the maximum number of people that can be fed and how the organization should allocate its money, we need to maximize the expression P = 1.1x + y - 108, where x represents the number of sacks of rice and y represents the number of sacks of beans. We have a budget of $1,800,000, and the costs of rice and beans are given as $38.50/sack and $35/sack, respectively. Let's set up the problem:

Total cost = (cost of rice) * x + (cost of beans) * y

$1,800,000 = $38.50x + $35y

We can rearrange this equation to solve for one variable in terms of the other:

y = (1,800,000 - $38.50x) / $35

Substitute this expression for y in the expression for P:

P = 1.1x + [(1,800,000 - $38.50x) / $35] - 108

Simplify the equation and combine like terms:

P = (1.1 - 38.50/35)x + (1,800,000/35) - 108

P = (-26.143)x + 51,428.571 - 108

P = (-26.143)x + 51,320.571

To find the maximum number of people that can be fed, we need to find the x-value that maximizes P. Since P is a linear function with a negative slope, it will be maximized at the smallest possible value of x. However, x should be a positive integer, so we can round up to the nearest integer value of x. In this case, x should be 1. With x = 1, we can calculate the corresponding value of y:

y = (1,800,000 - $38.50*1) / $35

y = 48,140

Therefore, the maximum number of people that can be fed is approximately 48,140, and the organization should allocate its money to buy 1 sack of rice and 48,140 sacks of beans.