I have started working on the problem below (please see bold) I need help (step by step) understanding how to solve this problem 4 A city council voted to conduct a study on inner city community problems using sociologists and research assistants from UMUC Allocation of time and costs per week are given in the following table Labor hours Sociologist Labor hours research assistant MINIMUM labor hours needed per week Fieldwork 10 30 180 Research center 20 10 160 Costs per week $500 $300 a How many sociologists and how many research assistants should be hired to MINIMIZE the cost and meet the weekly labor hour requirement b What is the MINIMUM weekly cost x sociologist, y research assistant, c total cost Fieldwork Constraints 10x 30y 180 Research Center Constraints 20x 10y 160 Non negative Constraints x,y 0 Objective Function C 500y 300y

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Question: I have started working on the problem below (please see bold). I need help (step by step) understanding how to solve this problem? 4.A city

I have started working on the problem below (please see bold). I need help (step by step) understanding how to solve this problem?

4.A city council voted to conduct a study on inner-city community problems using sociologists and research assistants from UMUC.Allocation of time and costs per week are given in the following table:

Labor hours - Sociologist

Labor hours research assistant

MINIMUM labor hours needed per week

Fieldwork

180

Research center

160

Costs per week

$500

$300

a.How many sociologists and how many research assistants should be hired to MINIMIZE the cost and meet the weekly labor-hour requirement?

b.What is the MINIMUM weekly cost?

x = sociologist, y = research assistant, c = total cost

Fieldwork Constraints 10x+30y>= 180

Research Center Constraints 20x+10y>=160

Non-negative Constraints x,y >= 0

Objective Function C= 500y+300y

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