Question

He XYZ Company produces two products. The total profit achieved from these products is described by the following equation:

Total profit = -0.2x₁² - 0.4X₂² + 8X₁ + 12X₂ + 1,500
Where:
X₁ = thousands of units of product 1
X₂ = thousands of units of product 2
Every 1,000 units of X₁ requires one hour of time in the shipping department, and every 1,000 units of X₂ requires 30 minutes in the shipping department.
Each unit of each product requires 2 pounds of a special ingredient, of which 64,000 pounds are available.
Additionally, 80 hours of shipping labor are available.
Demand for X₁ and X₂ is unlimited.
a. Formulated and NLP model for this problem.
b. Implement your model in a spreadsheet and solve it.
C. What is the optimal solution?

Answer 1

To formulate an NLP model for this problem, define the objective function, constraints, and decision variables. Implement the model in a spreadsheet using a solver tool to find the optimal solution. The optimal solution refers to the values of X₁ and X₂ that maximize the total profit.

Step-by-step explanation:

To formulate an NLP model for this problem, we need to define the objective function, constraints, and decision variables.

The objective function is the total profit, which is given as -0.2x₁² - 0.4X₂² + 8X₁ + 12X₂ + 1,500. The constraints are the availability of shipping hours and the special ingredients. The decision variables are X₁ (thousands of units of product 1) and X₂ (thousands of units of product 2).

To implement the model in a spreadsheet, you can create cells for the objective function, constraints, and decision variables.

Then use a solver tool to find the optimal solution by maximizing the total profit. The optimal solution will provide the values of X₁ and X₂ that maximize the profit.

The optimal solution refers to the values of X₁ and X₂ that maximize the total profit. It can be found by solving the NLP model using a solver tool in the spreadsheet.

Once the optimal solution is obtained, you can plug in the values of X₁ and X₂ into the objective function to calculate the maximum total profit.