(a)
To calculate: The objective function representing his weekly income for tutoring x hours of chemistry and y hours of math, if John makes$
(b)
To calculate: The system of inequalities representing the constraints.
The number of hours spent tutoring each subject cannot be negative.
Due to academic demands of his own classes he tutors at most
The tutoring center requires that he tutor mathematics at least
The demand for math tutor is greater than the demand for chemistry tutor. Therefore, the number of hours he spends tutoring mathematics must be at least twice the number of hours he spends tutoring chemistry.
(c)
To graph: The system of inequalities represented by the constraints.
The number of hours spent tutoring each subject cannot be negative.
Due to academic demands of his own classes he tutors at most
The tutoring center requires that he tutor mathematics at least
The demand for math tutor is greater than the demand for chemistry tutor. Therefore, the number of hours he spends tutoring mathematics must be at least twice the number of hours he spends tutoring chemistry.
(d)
To calculate: The vertices of the feasible region.
The number of hours spent tutoring each subject cannot be negative.
Due to academic demands of his own classes he tutors at most
The tutoring center requires that he tutor mathematics at least
The demand for math tutor is greater than the demand for chemistry tutor. Therefore, the number of hours he spends tutoring mathematics must be at least twice the number of hours he spends tutoring chemistry.
(e)
To calculate: The objective function at each vertex.
The number of hours spent tutoring each subject cannot be negative.
Due to academic demands of his own classes he tutors at most
The tutoring center requires that he tutor maths at least
The demand for math tutor is greater than the demand for chemistry tutor. Therefore, the number of hours he spends tutoring maths must be at least twice the number of hours he spends tutoring chemistry.
(f)
To calculate: The number of hours tutoring mathematics and tutoring chemistry should Josh workto maximize his income.
(g)
To calculate: The maximum profit for the instructions.
The number of hours spent tutoring each subject cannot be negative.
Due to academic demands of his own classes he tutors at most
The tutoring center requires that he tutor mathematics at least
The demand for math tutor is greater than the demand for chemistry tutor. Therefore, the number of hours he spends tutoring mathematics must be at least twice the number of hours he spends tutoring chemistry.
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