Question

Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have oak tops and more expensive hardware and require additional time for finishing and polishing. Standard desks require 70 board feet of pine and 10 hours of labor, whereas deluxe desks require 60 board feet of pine, 18 square feet of oak, and 15 hours of labor. For the next week, the company has 5,000 board feet of pine, 750 square feet of oak, and 400 hours of labor available. Standard desks net a profit of $225, and deluxe desks net a profit of $320. All desks can be sold to national chains such as Staples or Office Depot.

Identify the decision variables, objective function, and constraints in simple verbal statements.

Answer 1

The decision variables are the number of standard and deluxe desks produced. The objective function is to maximize profit. The constraints include the availability of resources such as pine, oak, and labor.

Step-by-step explanation:

The decision variables in this problem are the number of standard desks produced and the number of deluxe desks produced. The objective function is to maximize profit. The constraints include the availability of pine, oak, and labor.

The decision variables can be represented by the variables 'x' and 'y', where x represents the number of standard desks and y represents the number of deluxe desks.

The objective function can be written as: Maximize 225x + 320y, where 225 represents the profit from each standard desk, and 320 represents the profit from each deluxe desk.

The constraints can be written as: 70x + 60y ≤ 5000 (pine constraint), 18y ≤ 750 (oak constraint), and 10x + 15y ≤ 400 (labor constraint).

Answer 2

The decision variables are the two types of desks (standard x and deluxe y) to be produced. The objective function is to maximize total profit (225x + 320y). The constraints are based on the availability of pine, oak, and labor hours.

Step-by-step explanation:

The student's question involves identifying the decision variables, objective function, and constraints for a linear programming problem involving Burger Office Equipment's production of desks.

The decision variables for this scenario would be the number of standard desks (let's call this x) and the number of deluxe desks (let's call this y) to produce.

The objective function is the total profit, which is calculated as (225x + 320y), where 225 is the profit per standard desk, and 320 is the profit per deluxe desk.

The constraints are defined by the available resources for production:

• 5,000 board feet of pine: 70x + 60y ≤ 5,000,
• 750 square feet of oak: 18y ≤ 750,
• 400 hours of labor: 10x + 15y ≤ 400.

All desks can be sold, so there is no sales constraint mentioned in the problem.