# (Solved Homework): Problem Implement the linear optimization model that you developed for Burger Office…

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(This probelm is a number 7 of chapter 13 in Business analytics 2ed)

Problem Implement the linear optimization model that you developed for Burger Office Equipment in Problem in Excel and use Solver to find an optimal solution. Interpret the Solver Answer report and identify the binding constraints and verify the values of the slack variables by substituting the optimal solution into the model constraints Problem 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. a. Identify the decision variables, objective function, and constraints in simple verbal statements b. Mathematically formulate a linear optimization model.

The required simple verbal statements as follows :

Decision variables : Number of each type of desks which must be sold under standard and Deluxe category

Objective function : To Maximize total profit by selling designated number of standard and deluxe desks

Constraints :

Following are the different types of constraints :

1. The total quantity of pine required should not be more than 5000 board feet of Pine available
2. The total quantity of oak required should not be more than 750 square feet of Oak available
3. Total labour hours required for both products together should not be more than 400 hours of labor available

Let required number of desks to be produced as follows :

Standard desks = S numbers

Deluxe desks = D numbers

Where, S, D > = 0

Objective function :

Profit from S number of Standard desks = Profit per desk x Number of desks = \$ 225.S

Profit from D number of deluxe desks = Profit per desk x Number of desks = \$ 320.D

Therefore total profit earned , \$ = 225S + 320D

Since, objective is to maximize profit,

Thus the objective function is = Z = Maximize ( 225.S + 320D)

Constraint function :

S, D > = 0

1. Total quantity of Pine required for standard desks = 70.S

Total quantity of Pine required for deluxe desks = 60.D

Therefore,

Total quantity of Pine required = 70S + 60D Board feet of Pine

Since , maximum available Pine = 5000 board feet of Pine ,

70S + 60D < = 5000

1. Total quantity of Oak required = 18D square feet of Oak

Since , maximum available Oak = 750 square feet

Therefore , 18D < = 750

1. Total amount of labor hours required for S number of standard desks = 10.S

Total amount of labor hours required for D number of deluxe desks = 15.D

Thus total amount of labor hours required = 10S + 15.D hours

Since maximum available labor hours would be 400 hours

Therefore ,

10.S + 15.D < = 400

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