I need help finding constraints to put this on the graph. the objective function is c=16x+25y.
Problem: Your club plans to raisse money by selling two sizes of fruit baskets. The plan is to buy small baskets for $10 and sell them for $16, and to buy large baskets for $15 and sell them for $25. The club president estimates that you will not sell more than 100 baskets. Your club can afford up to $1200 to buy baskets. Find the number of small and large baskets you should buy in order to maximize profit.
This is a Linear Programming Problem
Plot small baskets on vertical axis, large on the horizontal axis.
Constraints: x, nor y can be less than zero. x+y=100.
and finally, 10y + 15x<=1200
So, plot the lines y=-x + 100, then y=120-1/5x
Now test the corners for profit. Remember Profit is income-costs. At one of the corners, you will get max profit.
let x = number of small baskets
let y = number of large baskets
There are two constraints given:
"The club president estimates that you will not sell more than 100 baskets."
The total number of baskets <= 100: so x + y <= 100
"Your club can afford up to $1200 to buy baskets."
10x + 15y <= 1200, because the cost of buying one small basket is $10, and the cost of buying one large basket is $25
Note that profit is p= (16-10)x + (25-15)y because you have to buy the baskets.
420x2=
and estimate by rounding to the largest place:4587
-2695
To solve this linear programming problem, we need to define the constraints and the objective function.
Let's start by defining the decision variables:
x = number of small baskets to buy
y = number of large baskets to buy
Now, let's define the constraints based on the given information:
1. The total number of baskets should not exceed 100.
x + y <= 100
2. The club can afford up to $1200 to buy baskets.
10x + 15y <= 1200
3. The number of baskets cannot be negative.
x >= 0
y >= 0
Next, let's define the objective function, which is the profit:
c = 16x + 25y
The objective is to maximize the profit, which means we want to find the values of x and y that will maximize the value of c.
By adding all the constraints and the objective function together, we get the complete linear programming problem:
Maximize c = 16x + 25y subject to the following constraints:
x + y <= 100
10x + 15y <= 1200
x >= 0
y >= 0
Now, you can solve this linear programming problem using various methods such as graphical method, simplex method, or computer software.