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# Scenario 1: Sylvia is looking for the best option for daycare for her child. A home-based option charges a flat rate per hour. A center-based option...

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Scenario 1: Sylvia is looking for the best option for daycare for her child. A home-based option charges a flat rate per hour. A center-based option charges a fixed fee per week for a certain number of hours and then a fixed rate per hour for any hour provided over the set amount. Determine which option is most advantageous for the parent based upon the parents’ needs. Task A 1 . Mrs. Sylvia is trying to find a day care center for her only child and she selected two options after looking at a handful of options: Day Care Center A (DCCA) Day Care Center B (DCCB) DCCA charges \$30/hour and DCCB charges a fixed amount of \$1000 for a block of 30 hours and \$20/hour for overstay beyond the 30 hours limit. The total cost charged by DCCA is: Cost= #hours * \$30 The total cost charged by DCCB is: Cost = \$1000 + 20* (if #TotalHours>30((#TotalHoursMonth -30),1) Where #TotalHoursMonth is the stay period calculated within a month and if the total is greater than 30 it will be subtracted by 30 which is the size of the package that DCCB offers. In case the #TotalHoursMonth is less than 30 hours (which means that the child stayed less time than was paid for) 2. Although the cost is important in order to make sure it will fit her budget, Mrs. Sylvia is not only taking the financial aspect in consideration. She is also looking at the positive and negative reviews from a website that ranks Childcares in many different categories such as amenities, cleanliness, education and preparation level of the employees, reputation, emergency room availability and etc. These variables will also be put together and analyzed before she makes a final decision.
3. The DCCA charges for a more granular period and is a linear function of the number of hours used with a slope of \$30/hr. DDCB charges a fixed amount (\$1000) for a larger block of period (30 hours/week) plus a linear function of the number of hours overstayed on that week with a slope of \$20/hour. Task B 1. The Total Cost charged by DCCA is Cost= #hours*\$30 The total cost charged by DCCB is Cost = \$1000 + 20*(#hours -30) if #hours>30 Cost = \$1000, h <=30 2. The total cost function for DCCA is a linear function of the number of hours of service provided with a slope of \$30 per hour. DCCB’s total cost is a fixed amount of \$1,000 for services up to 30 hours/ week then a linear function of additional hours of day care services provided beyond 30 hours with slope of \$20/hour. 3. The comparison of the total cost charged by each company to find the number of hours of services where the total cost for Mrs. Sylvia is same independent of what Center she selects. To prove: 30 hours = \$1,000 + 20*(hours-\$30) 30 hours = \$1,000 + 20hours – \$600 30 hours -20hours = \$1,000 - \$600 10 hours = 400 = > \$40/hour This means that when the total number of hours of services provided for 40 hours / week, the total cost charged by both Centers is identical. This reasoning based on the 40 hours journey is possible by assuming #hours is equal to 40 in the total cost function for DCCA
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Scenario 1:
Sylvia is looking for the best option for daycare for her child. A home-based option charges a flat
rate per hour. A center-based option charges a fixed fee per week for a certain...

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