Question

Suppose that the costs are $900 if selecting project 1 to do, $800 if selecting project 2 to do, and $700 if selecting project 3 to do, respectively.Suppose that we have $2,000 available. Write a constraint to represent: "Total cost of doing selected projects cannot be more than $2,000", in terms of X₁, X₂, and X₃ as defined above

Answer 1

To express the budget constraint for the selected projects, the inequality 900X₁ + 800X₂ + 700X₃ ≤ $2,000 is used, indicating the sum cost of projects chosen must not go over the $2,000 budget.

Step-by-step explanation:

To represent the constraint "Total cost of doing selected projects cannot be more than $2,000", we can use the prices of the projects and the variables X₁, X₂, and X₃ to stand for the quantity (or decision to undertake) of each project. The cost for undertaking project 1 is $900, project 2 is $800, and project 3 is $700, respectively. So, the constraint in terms of X₁, X₂, and X₃ would be:

900X₁ + 800X₂ + 700X₃ ≤ $2,000

This equation expresses that the total expenditure on the selected projects, which is the sum of the individual costs multiplied by the decision variables (i.e., the quantity of each project selected), cannot exceed the available budget of $2,000.