Question

Formulate but do not solve a linear programming model for the following problem: A company makes square boxes and triangular boxes. Square boxes take 2 minutes to make and sell for a profit of $4. Triangular boxes take 3 minutes to make and sell for a profit of $5. The client wants at least 25 boxes and at least 5 boxes of each type ready in one hour. What is the best combination of square and triangular boxes so that the company makes the most profit from this client?

Answer 1

To formulate a linear programming model for this problem, assign variables for square boxes and triangular boxes, maximize the profit objective function, and set up constraints based on the given requirements.

Step-by-step explanation:

To formulate a linear programming model for this problem, let's assign the following variables:

S = number of square boxes

T = number of triangular boxes

We want to maximize the profit, so the objective function is:

Maximize Z = 4S + 5T

Now, let's set up the constraints:

Constraint 1: Square boxes take 2 minutes to make and we have 60 minutes, so: 2S <= 60

Constraint 2: Triangular boxes take 3 minutes to make and we have 60 minutes, so: 3T <= 60

Constraint 3: The client wants at least 25 total boxes, so: S + T >= 25

Constraint 4: The client wants at least 5 square boxes, so: S >= 5

Constraint 5: The client wants at least 5 triangular boxes, so: T >= 5

These are the constraints that need to be satisfied in order to formulate the linear programming model for this problem.