Robert Hope Received a Welcome Surprise in This Management Science

Robert Hope received a welcome surprise in this management science class;the instructor has decided to let each person define the percentage contribution to their grade for each of the graded instruments used in the class.These instruments were: homework,an individual project,a mid-term exam,and a final exam.Robert's grades on these instruments were 75,94,85,and 92,respectively.However,the instructor complicated Robert's task somewhat by adding the following stipulations:
• homework can account for up to 25% of the grade,but must be at least 5% of the grade;
• the project can account for up to 25% of the grade,but must be at least 5% of the grade;
• the mid-term and final must each account for between 10% and 40% of the grade but cannot account for more than 70% of the grade when the percentages are combined;and
• the project and final exam grades may not collectively constitute more than 50% of the grade.Formulate an LP model for Robert to maximize his numerical grade.