Practice MidT.xlsx

Minutes per garment Machine Shirt Pant Cutting 3 6 1413 Sewing 6 2 1218 Assembly 5 4 1317 Minutes Available 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.

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 Armitag car takes 50 minutes in Assembly-line 1, 90 minutes in Assembly-line 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 Armitag 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.

Armitage Bronny Available Assy 1 50 40 minutes 80 Assy 2 90 45 minutes 108 Assy 3 25 75 minutes 100 Min prod 25 cars Max prod 80% ttl cars Profit $1,020 $360 ge 2, s ge

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A brewery producing two types of beer has an algebraic model as shown. 1) Given the algebraic formulation, set up an Excel solver solution of the model an 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. (as it would appear in a problem description before transformation into standard form)?

\begin{array}{l} x_{1} \text{= the number of litres of lager made x_{2} \text{= the number of litres of ale made ea \end{array} \\ \\ \begin{array}{rl} \text{Maximize } & 1.2x_{1} + 0.9x_{2} \\ \text{subject to } \\ \text{production of lager } & 1x_{1} + 0x_{2} \g \text{production of ale} & 0x_{1} + 1x_{2} \ge 3 \text{total production } & 1x_{1} + 1x_{2} \le 80 \text{process 1} & 4x_{1} + 2x_{2} \le 22000 \\ \text{process 2} & 2x_{1} + 6x_{2} \le 38000 \\ \text{process 3} & 3x_{1} + 8x_{2} \le 50000 \\ \text{proportion} & 1x_{1} - 0.7x_{2} \le 0\\ \end{array} nd e

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