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