Question 1 (16 points) Sunview Restaurant is open from 8am to 10pm daily. Besides the hours...

Transcribed Image Text:

Question 1 (16 points) Sunview Restaurant is open from 8am to 10pm daily. Besides the hours they are open for business, workers are needed an hour before opening and an hour after closing for setup and clean-up activities. The restaurant hires both full-time and part-time workers. Each full-time worker works 8 hours a day with a pay rate of $10/hour. Each part-time worker works 4 hours a day with a pay rate of $8/hour. The restaurant operates on the following shifts: Shifts 7am - 11am 7am - 3pm 11am - 3pm 11am - 7pm 3pm-7pm 3pm - 11pm 7pm 11pm The following numbers of workers are needed during each of the indicated time blocks: Hours 7am - 11am 11am 1pm 1pm - 3pm Workers Needed 11 25 16 - 3pm 5pm 10 5pm - 7pm 22 7pm - 9pm 17 9pm - 11pm 6 At least one full time worker must be available during the hour before opening and after closing. Additionally, at least 40% of the employees should be full-time workers during the restaurant's busy periods from 11am - 1pm and 5pm - 7pm. The restaurant wants to determine an employee schedule to minimize total daily labor costs. Formulate a linear programming model for this problem. You need to define decision variables, and write the objective function and all constraints. Please write your final version of the objective function and constraints in linear forms. If some constraints have non-linear forms before you transform them into linear forms, I suggest that you write both initial and final versions of these constraints. Do not abbreviate your formulation. Question 1 (16 points) Sunview Restaurant is open from 8am to 10pm daily. Besides the hours they are open for business, workers are needed an hour before opening and an hour after closing for setup and clean-up activities. The restaurant hires both full-time and part-time workers. Each full-time worker works 8 hours a day with a pay rate of $10/hour. Each part-time worker works 4 hours a day with a pay rate of $8/hour. The restaurant operates on the following shifts: Shifts 7am - 11am 7am - 3pm 11am - 3pm 11am - 7pm 3pm-7pm 3pm - 11pm 7pm 11pm The following numbers of workers are needed during each of the indicated time blocks: Hours 7am - 11am 11am 1pm 1pm - 3pm Workers Needed 11 25 16 - 3pm 5pm 10 5pm - 7pm 22 7pm - 9pm 17 9pm - 11pm 6 At least one full time worker must be available during the hour before opening and after closing. Additionally, at least 40% of the employees should be full-time workers during the restaurant's busy periods from 11am - 1pm and 5pm - 7pm. The restaurant wants to determine an employee schedule to minimize total daily labor costs. Formulate a linear programming model for this problem. You need to define decision variables, and write the objective function and all constraints. Please write your final version of the objective function and constraints in linear forms. If some constraints have non-linear forms before you transform them into linear forms, I suggest that you write both initial and final versions of these constraints. Do not abbreviate your formulation.