Robert Hope Received a Welcome Surprise in This Management Science $25 \%$

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:
-homewark can account far up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade;
-the praject can account for up to $25 \%$ of the grade, but must be at least $5 \%$ af the grade;
-the mid-term and final must each accaunt far betwen $10 \%$ and $40 \%$ of the grade but cannot accaunt far mare than $7 \%$ of the grade when the percentages are cambined; and
-the project and final exam grades may not collectively constitute more than $50 \%$ of the Iratade. Formulate an LP model for Robert to maximize his numerical grade.