Roberta Hernandez sells three items‐A, B, and C in her gift shop. Each unit of A costs her $2
to buy, $1 to sell, and $2 to deliver. For each unit of B, the costs are $3, $2, and $2, respectively,
and for each unit of C, the costs are $6, $2, and $4 respectively. The profit on A is $4, on B it is
$3, and on C $3. How many of each item should she order to maximize her profit if she can
spend $1200 to buy, $800 to sell, and $500 to deliver?
Matt, Help -- please use the same name for your posts.
sorry...can you still help me though?
To solve this problem, we can use linear programming to determine the optimal quantities of items A, B, and C to order.
Let's denote the number of units of item A, B, and C ordered as x, y, and z respectively.
The objective is to maximize the profit, which is given by:
Profit = (Profit per unit of A * Number of units of A) + (Profit per unit of B * Number of units of B) + (Profit per unit of C * Number of units of C)
Profit = (4x) + (3y) + (3z)
Now, let's consider the constraints:
Cost to buy: (Cost per unit of A * Number of units of A) + (Cost per unit of B * Number of units of B) + (Cost per unit of C * Number of units of C) ≤ $1200
2x + 3y + 6z ≤ 1200
Cost to sell: (Cost to sell per unit of A * Number of units of A) + (Cost to sell per unit of B * Number of units of B) + (Cost to sell per unit of C * Number of units of C) ≤ $800
1x + 2y + 2z ≤ 800
Cost to deliver: (Cost to deliver per unit of A * Number of units of A) + (Cost to deliver per unit of B * Number of units of B) + (Cost to deliver per unit of C * Number of units of C) ≤ $500
2x + 2y + 4z ≤ 500
Additionally, the quantities of items cannot be negative:
x ≥ 0, y ≥ 0, z ≥ 0
Now, we can solve this linear programming problem using optimization techniques. The specific method used will depend on the software or tools available to you. This can be done with mathematical optimization software such as Microsoft Excel or MATLAB, or programming languages with optimization libraries such as Python with SciPy or R with the lpSolve package.
The solution to this problem will give you the optimal quantities of items A, B, and C to order in order to maximize the profit while staying within the given budget constraints.