Pls help me formulate a linear programming model for this problem. Pls state the

Question

Pls help me formulate a linear programming model for this problem. Pls state the following respectively:

1. Decision Variables

2. Objective function

3. Constraints

Pls. Make the solution neat, organized, and student friendly :)

Pls Clarify the decision variables, objective function, and constraints. If you have a diferent solution to the problem, please make it clear and explained. Thanks for the patience

58* To process income tax forms, the IRS first sends each form through the data preparation (DP) department, where information is coded for computer entry. Then the form is sent to data entry (DE), where it is entered into the computer During the next three weeks, the following number of forms will arrive: week 1, 40,000; week 2, 30,000; week 3, 60,000 The IRS meets the crunch by hiring employees who work 40 hours per week and are paid $200 per week. Data preparation of a form requires 15 minutes, and data entry of a form requires 10 minutes. Each week, an employee is assigned to either data entry or data preparation. The IRS must complete processing of all forms by the end of week and wants to minimize the cost of accomplishing this goal. Formulate an LP that will determine how many workers should be working each week and how the workers should be assigned over the next five weeks

Explanation / Answer

Objective and decision variables

Objective means we want to choose maximize or minimize, question itself mention minimize the cost, so objective is minimize.

Decision variables:

Variables appear in objective function: In this case, x1+x2 are variables

Constraints:

Which used for express the relations betwee varibales.

Minimize : x1+x2=$200

Constraint:

15pd1+10d2=week1

15pd1+10d2=week2

15pd1+10d2=week3

15pd1+10d2=week4

15pd1+10d2=week5

Constraints:

15pd<2400

15pd<2400

15pd<2400

15pd<2400

15pd<2400

10d2<2400

10d2<2400

10d2<2400

10d2<2400

10d2<2400

15pd1+10d2<140,000

15pd1+10d2>230,000

15pd1+10d2>360,000

15pd1+10d2=bal1,2,3

15pd1+10d2=bal1,2,3

pd1+ed2<0.

pd= data preparation 15 min per form

ep=data entry.10 min per form

a employee can do either data preparationd or data entry per day.

so   each work shown separately    for 5 weeks

upto 3 weeks forms will be received but completed within 5 weeks, mentioned balance form to be completed from 4 and 5 week.

Explanation

b1,2,3=    Balance from 1st and 2nd and 3rd week. needs to be completed 4 and 5th week

2400 = 60 minutes per week *40 hours per week =2400 minutes work to be done per week

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