9. 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?
Isn't this an exam problem? http://www.assignmenthelpexperts.com/sample/Operation-Homework-Help-Sample.pdf
no this is a worksheet for our final... I really don't understand how to do it.
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To find the optimal number of each item that Roberta should order to maximize her profit, we need to set up a linear programming problem.
Let:
- x be the number of units of item A to order
- y be the number of units of item B to order
- z be the number of units of item C to order
We want to maximize the profit, which is given by the equation:
Profit = 4x + 3y + 3z
However, there are constraints that we need to consider:
1. The total cost to buy the items should not exceed $1200:
2x + 3y + 6z ≤ 1200
2. The total cost to sell the items should not exceed $800:
x + 2y + 2z ≤ 800
3. The total cost to deliver the items should not exceed $500:
2x + 2y + 4z ≤ 500
Now, we have a linear programming problem. We want to maximize the profit function with the given constraints.
To solve this problem, you can use software such as Microsoft Excel or Google Sheets that have built-in linear programming solver functions. Here are the steps to solve this problem in Microsoft Excel:
Step 1: Set up the spreadsheet
- Create a new spreadsheet and label the columns as follows: A, B, C, Profit, Cost to Buy, Cost to Sell, Cost to Deliver.
- Fill in the table with the given values for each item.
Step 2: Set up the objective function and constraints
- In a new row, below the table, enter the coefficients of the objective function (Profit) in the corresponding columns (4 in cell E9, 3 in cell F9, 3 in cell G9).
- In the rows below the objective function row, enter the coefficients of each constraint.
Step 3: Install the Solver Add-in
- Go to the "File" menu, then click on "Options."
- In the Excel Options dialog box, select "Add-Ins" from the left sidebar.
- In the "Manage" section at the bottom, select "Excel Add-ins" and click on "Go."
- In the Add-Ins dialog box, check the box for "Solver Add-in" and click on "OK."
Step 4: Set up the Solver
- Go to the "Data" tab, then click on "Solver" in the "Analysis" group.
- In the Solver Parameters dialog box, set the following options:
- Set the "Set Objective" field to the cell where the total profit is calculated (E9 in this case).
- Select "Max" from the "To" dropdown list.
- In the "By Changing Variable Cells" field, select the range of cells representing the variables (x, y, z values).
- In the "Subject to the Constraints" section, add each constraint by selecting the corresponding range of cells.
- Click on "OK" to close the dialog box.
Step 5: Solve the problem
- Click on the "Solve" button in the Solver Parameters dialog box.
- Solver will calculate the optimal values for x, y, and z that maximize the profit, while satisfying the constraints.
After the Solver has finished, it will display the optimal values for x, y, and z, as well as the maximum profit.
Please note that the Solver function may not be available in all versions of Excel or other spreadsheet software, in which case you might need to use specialized optimization software or programming languages like Python to solve the linear programming problem.