need help with this question please

PART A: Answer Question A1 in this section of the paper. Question A1 (25 marks) Skein Sports sell freshly made protein bars. They are made up each morning and delivered by a local bakery delivery service. Skeinsports orders 60 of these bars each day but the amount they actually receive varies because of the high demand for the bars at other stores and the delivery service being unreliable. Sometimes the bakery is not able to deliver at all and so Skeinsports receives no protein bars. This happens randomly but on average it occurs on one out of every seven days. When the bakery does make a delivery they are not always able to supply the full order of 60 bars; the number actually delivered follows the probability distribution: Number of bars supplied 52 56 60 Probability 0.05 0.15 0.35 0.27 0.18 Skein Sports is open every day with a similar demand for protein bars each day. The probability distribution for daily demand is: 45 50 55 60 65 Demand Probability 0.12 0.25 0.40 0.16 0.07 The protein bars must be sold on the day that they are supplied or on the following day. The label on each bar shows the day on which it was made, and customers will only buy the previous day's bars if all of today's bars have been sold. Any bars from the previous day that are not sold are thrown away. If the demand on a given day is more than the number of bars available then the excess demand is lost sales. (a) Explain how you would use random numbers to model the variability is this situation (20% marks) (b) Simulate this situation for 7 days and show for each day the number of protein bars sold and thrown away as well as the number of lost sales. Use the table of random numbers provided in the formula sheet using the following rows for the individual distributions: Row 1 for the delivery random numbers, Row 2 for the amount delivered random numbers, Row 3 for the demand random numbers. Assume that there are 10 bars from the previous day in stock at the start of the simulation 40% marks) (c) What is the average number of lost sales over the 7 days simulated in part b? Given this estimate, what action would you advise Skein Sports take? How might this estimate be improved? (10% marks) (d) The company is considering changing supplier to a larger bakery who are more expensive but are very reliable and will always be able to deliver the amount ordered. If they change to the larger bakery they may also decide to change the quantity that they order. Explain how the company could use a simulation model to determine the best quantity or protein bars to order from the larger bakery. (15% marks) le) In general, simulation is used as an alternative to experimenting with the real system Explain the general advantages of using a simulation model rather than experimenting with the real system (15% marks) PART A: Answer Question A1 in this section of the paper. Question A1 (25 marks) Skein Sports sell freshly made protein bars. They are made up each morning and delivered by a local bakery delivery service. Skeinsports orders 60 of these bars each day but the amount they actually receive varies because of the high demand for the bars at other stores and the delivery service being unreliable. Sometimes the bakery is not able to deliver at all and so Skeinsports receives no protein bars. This happens randomly but on average it occurs on one out of every seven days. When the bakery does make a delivery they are not always able to supply the full order of 60 bars; the number actually delivered follows the probability distribution: Number of bars supplied 52 56 60 Probability 0.05 0.15 0.35 0.27 0.18 Skein Sports is open every day with a similar demand for protein bars each day. The probability distribution for daily demand is: 45 50 55 60 65 Demand Probability 0.12 0.25 0.40 0.16 0.07 The protein bars must be sold on the day that they are supplied or on the following day. The label on each bar shows the day on which it was made, and customers will only buy the previous day's bars if all of today's bars have been sold. Any bars from the previous day that are not sold are thrown away. If the demand on a given day is more than the number of bars available then the excess demand is lost sales. (a) Explain how you would use random numbers to model the variability is this situation (20% marks) (b) Simulate this situation for 7 days and show for each day the number of protein bars sold and thrown away as well as the number of lost sales. Use the table of random numbers provided in the formula sheet using the following rows for the individual distributions: Row 1 for the delivery random numbers, Row 2 for the amount delivered random numbers, Row 3 for the demand random numbers. Assume that there are 10 bars from the previous day in stock at the start of the simulation 40% marks) (c) What is the average number of lost sales over the 7 days simulated in part b? Given this estimate, what action would you advise Skein Sports take? How might this estimate be improved? (10% marks) (d) The company is considering changing supplier to a larger bakery who are more expensive but are very reliable and will always be able to deliver the amount ordered. If they change to the larger bakery they may also decide to change the quantity that they order. Explain how the company could use a simulation model to determine the best quantity or protein bars to order from the larger bakery. (15% marks) le) In general, simulation is used as an alternative to experimenting with the real system Explain the general advantages of using a simulation model rather than experimenting with the real system (15% marks)