W0 = N &= WM A B C D E F G H I A factory makes shirts and pants. Each shirt yields a profit of $2, while each pant gives a profit of $3. They can sell at most 190 pants. Each garment spends time on three machines as shown in the table. The number of pants must be at least 30% of the total number of garments made. 1) Formulate an algebraic model to this scenario. Make sure the objective function and constraints are in standard form (linear combination of coefficients and variables on the left hand side and no variables on the right hand side). 2) Insert an excel graph on this sheet and add the constraints, an isoprofit line, and highlight the feasible region. Minutes per garment W~ @ e L R e MR R R e e e e e e B O W@ u R W N e o A B c D E F G H 1 ] A company makes two models of cars, called the Armitage and the Bronny models. After deducting all direct costs, each Armitage car gives a profit of $1020, while each Bronny car gives a profit of $360. There is a contractual obligation to produce at least 25 Armitage cars per week. Every car goes through three assembly-lines. Every Armitage car takes 50 minutes in Assembly-line 1, 90 minutes in Assembly-line 2, and 25 minutes in Assembly- line 3. Every Bronny car takes 40 minutes in Assembly-line 1, 45 minutes in Assembly-line 2, and 75 minutes in Assembly-line 3. Every week, Assembly-lines 1, 2, and 3 are open 80, 108, and 100 hours respectively. They want the production of Armitage cars to be no more than 80% of the total production. 1) Formulate an algebraic model to this scenario. Make sure the objective function and constraints are in standard form (linear combination of coefficients and variables on the left hand side and no variables on the right hand side). 2) Insert an excel graph on this sheet and add the constraints, an isoprofit line, and highlight the feasible region. minutes minutes minutes Available A B C D E F G H K L M N O P Q R S T U A brewery producing two types of beer has an algebraic model as shown. x1= the number of litres of lager made each day 72= the number of litres of ale made each day 1) Given the algebraic formulation, set up an Excel solver solution of the model and find the optimal values for X1 and X2. 2) Describe your optimal model includeing final values and binding constraints. 3) Extra Credit: how would you calculate the actual proportion that resulted in the proportion constraint. Maximize 1.2x1 + 0.9x2 (as it would appear in a problem description before transformation into standard form)? subject to 10 production of lager 1x1 + 0x2 2 2000 11 production of ale Ox1 + 1x2 2 3000 12 13 total production lx1 + 1x2