The Timex Shop has just received four new projects that must be completed quickly, i$.$e$.,$ project $1,$ project $2,$ project $3,$ and project $4.$ Four workers namely Amrita, Barun, Chetan, and Devi with different talents will be able to do the job. Amrita, Barun, Chetan, and Devi can be assigned to any of these projects. It is known that every project will comprise only one worker. Also, one worker will work on only one project and will not change the project after the assignment. The wages charged by the workers in different projects are given below in the following table

Workers Projects

Project $1$ Project $2$ Project $3$ Project $4$

Amrita $$10$ $$40$ $$60$ $$30$

Barun $$90$ $$70$ $$100$ $$90$

Chetan $$40$ $$50$ $$110$ $$70$

Devi $$80$ $$70$ $$80$ $$50$

Now, Timex Shop wants to complete all of these projects at minimum cost. Based on the information

given above, answer the following questions. Also, clearly write down each of the steps.

a$)$ Write down linear programming for this assignment problem consistent with the objective of Fix-itt Shop

b$)$ Using the Hungarian method, determine the optimal assignment of the workers that will minimize the cost $($Use manual process$)$

c$)$ What is the minimum cost incurred by Timex Shop as per Hungarian method?