inear programming. The course grade is composed or the following components: midterm exam score, final exam score, individual assignments score, and class participation score. Cory Just received their final exam maximize their total score, subject to the following restrictions:

The participation score weight can be no more than $0\mathrm{.}25.$

The midterm, final, and assignments score weights can be no more than $0\mathrm{.}6.$

The miaterm exam score weight must be at least twice as much as the participation weight.

The final exam score weight must be at least three times as much as the participation weight.

The weight for each of the four components must be at least $0\mathrm{.}10.$

The weights used for each component must be nonnegative and the four weights must sum to one.

Cory has decided to try to maximize their grade.

$($a$)$ Formulate and solve the model that could be used to maximize Cory's total score. If the constraint is one, enter $"1^{\text{'}}.$ If the amount is zero, enter $"0".$ For negative numbers use a minus sign $($Example: enter $-100).$

Let $w_1=$ weight placed on the midterm exam

$w_2=$ weight placed on the final exam

$w_3=$ weight placed on the individual assignments

$w_4=$ weight placed on class participation

$\backslash$table$[[$Max$,w_1+,w_2+,w_3+,w_4,$Objective function$],[$s$.$t$.],[,w_1+,w_2+,w_3+,$w$4-$ Select your answer $-V,$Maximum midterm weight$],[,w_1+,w_2+,w_3+,$wa $-$ Select your answer $-V,$Maximum final weight$],[,w_1+,w_2+1,w_3+,$wa $-$ Select your answer $-V,$Maximum assignments weight$],[,w_1+,]w_2+1,|w_3+|,$wa $-$ Select your answer $-V,$Maximum participation weight$],[,w_1+,w_2+,w_3+,$wa $-$ Select your answer $-V,$Minimum miaterm weight$],[,w_1+,w_2+1,|w_3+|,$wa $-$ Select your answer $-V,$Minimum final weight$],[,w_1+,w_2+1,{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{w}_3+,$wa $-$ Select your answer $-V,$Minimum assignments weight$],[,w_1+,|w_2+1|,w_3+,$w$4-$ Select your answer $-V,$Minimum participation weight$],[,w_1+,w_2+,w_3+,$wa $-$ Select your answer $-V,$Midterm weight at least twice participation weight$],[,w_1+,w_2+,w_3+,$wa $-$ Select your answer $-V,$Final weight at least three times participation weight$],[,w_1+,w_2+,n_3+,$wa $-$ Select your answer $-V,$Total weight$],[,,,,,w4,$nonnegativity condition$]]$