Answer: The system of linear inequalities to model the number of hours that you could work at each location in a week are,
Subject : 5x+7y,
[tex]x+y\leq 15[/tex] and [tex]x\geq 4[/tex], where x represents number of hours in tips working at a video store and y represents number of hours working at a landscaping company.
Step-by-step explanation:
Let x represents number of hours in tips working at a video store and y represents number of hours working at a landscaping company.
Therefore total cost which have to be maximized,
Z= 5x+7y,
Now, we must work at least four hours per week at the video store,
Therefore, [tex]x\geq 4[/tex]
And, the total number of hours you work at both jobs and weak cannot be greater than 15.
Therefore, [tex]x+y\leq 15[/tex]
Thus, the required system of equation is, Z= 5x+7y, [tex]x+y\leq 15[/tex] , [tex]x\geq 4[/tex],
Since, at ( 4,11) Z= 97 which is maximum value.
Thus the solution of the above system of equation is x=4 and y=11.
