Burger Office Equipment produces two types of desks, standard and deluxe. Deluxe desks have oak toos and more-expensive hardware and require additional time for finishing and polishing. Standard desks require 75 board feet of pine and 10 hours of labor, whereas deluxe desks require 60 board feet of pine, 20 square feet of oak, and 16 hours of labor. For the next week, the company has 3,960 board feet of pine, 800 square feet of oak, and 736 hours of labor available. Standard desks net a profit of $270, and deluxe desis net a profit of $360. All desks can be sold to national chains like Staples or Office Depot. Determine how many standard and deluce desiks are to be produced in order to maximize the total profit. Use the notebook homework7Pr1.Rmd file posted on Sakai for this probiem. (1) Formulate the linear programming model for this problem. a. Define the decision variables b. Formulate the objective function c. State the constraints (2) Entering the problem data and finding the optimum solution using R Studio a. Install the ipsolve attachment if you have not installed it before Install attachments ("IpSolve") b. Call IpSolve library Lbrary (lpsolve) c. Enter the problem Data (formulation) d. Solution (i) Solve the problem (ii) Display the optimum solution values? How many standard desks are to be produced? How many deluxe desks are to be produced? (iii) Display the objective function value (total profit) of the optimum solution? What is the total profit? e. Obtain the dual values. f. Answer the following questions about the dual values: (i) What do the dual values for each source: pine, oak, and labor? What do they indicate? (ii) How much would the profit increase if the company had one more board foot of pine? (iii) How much would the profit increase if the company had one more board foot of oak? (iv) How much would the profit increase if the company had one more labor hour? (v) If the company could purchase additional board foot of pine for $150, should the company purchase any? Why? (v) If the company can hire labor for $15 per hour, should the compamy hire any with this cost? Why