Scenario: Sarah wants to establish an online business selling custom clothes. She can allocate a maximum...

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Scenario: Sarah wants to establish an online business selling custom clothes. She can allocate a maximum of 60 hours per week to her venture. Crafting a shirt takes 6 hours, a jacket 7 hours, and underwear 4.5 hours. Sarah can purchase up to 90 yards of fabric per week at $1.25 per yard, and she must buy at least 10 yards of specialty fabric at $2.00 per yard. She can acquire as much thread as needed to create her products. Each shirt requires up to 2 yards of fabric, jackets need 3 yards, and underwear use 1.5 yards. Sarah can sell a maximum of 15 clothes each week and wishes to avoid overproduction. There's also an online fee per sold item, for which she sets aside $50. Her costs include $3 per shirt, $2 per jacket, and $1.50 per underwear. In terms of profit, Sarah gains $10 for each shirt, $12 for each jacket, and $6.50 for every underwear. Sarah's primary objective is to calculate the optimal quantities of shirts, jackets, and underwear to craft each week to maximize her overall profits. Objective: Sarah aims to maximize her weekly profits from selling shits, jackets, and underwear online, considering constraints on production time, material availability, sales limits, and associated costs. Quantitative method: Linear Programming Tasks: 1. Define decision variables. 2. Formulate the objective function. 3. Set up constraints. 4. Solve the Linear programming problem. 5. Interpret the solution. Possible results, conclusions and recommendations: Scenario: Sarah wants to establish an online business selling custom clothes. She can allocate a maximum of 60 hours per week to her venture. Crafting a shirt takes 6 hours, a jacket 7 hours, and underwear 4.5 hours. Sarah can purchase up to 90 yards of fabric per week at $1.25 per yard, and she must buy at least 10 yards of specialty fabric at $2.00 per yard. She can acquire as much thread as needed to create her products. Each shirt requires up to 2 yards of fabric, jackets need 3 yards, and underwear use 1.5 yards. Sarah can sell a maximum of 15 clothes each week and wishes to avoid overproduction. There's also an online fee per sold item, for which she sets aside $50. Her costs include $3 per shirt, $2 per jacket, and $1.50 per underwear. In terms of profit, Sarah gains $10 for each shirt, $12 for each jacket, and $6.50 for every underwear. Sarah's primary objective is to calculate the optimal quantities of shirts, jackets, and underwear to craft each week to maximize her overall profits. Objective: Sarah aims to maximize her weekly profits from selling shits, jackets, and underwear online, considering constraints on production time, material availability, sales limits, and associated costs. Quantitative method: Linear Programming Tasks: 1. Define decision variables. 2. Formulate the objective function. 3. Set up constraints. 4. Solve the Linear programming problem. 5. Interpret the solution. Possible results, conclusions and recommendations: