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1:47 Up MOO Question . . . Question 3. A department store sells sets of Bluetooth headphones. The sales of the headphones over the last 200 days are detailed in the table below: Sales Number of Days Sales Number of Days 0 8 6 30 12 7 26 2 18 8 12 3 20 9 8 4 24 10 4 5 38 Each order of headphones comprises 30 sets of headphones and costs the store $75, payable on making the order. 75% of the time the order arrives on the morning two days after the order is placed, otherwise it arrives on the morning four days after the order is placed. The store is charged $1.25 per set of headphones per day to insure any stock it is holding. If the store runs out of headphones it estimates a lost-sales cost of $60 per set. At the moment the store orders headphones every 5 days resulting in a mean daily cost of $65. (a) Produce probability distribution functions for headphone sales and order arrival. Allocate rand to th distributions. (4 marks) O O1:48 Up M {9 G3 'o'"lu. \"'8?\" .. 395'- 6 Question / III A department store sells sets of Bluetooth headphones. The sales of the headphones over the last 200 days are detailed in the table below: W WM 15'. o 8 6 30 1 12 7 26 2 18 8 12 3 20 9 8 4 24 1o 4 5 38 Each order of headphones comprises 30 sets of headphones and costs the store $75, payable on making the order. 75% of the time the order arrives on the morning two days after the order is placed, otherwise it arrives on the morning four days after the order is placed. The store is charged $1.25 per set of headphones per day to insure any stock it is holding. If the store runs out of headphones it estimates a lost-sales cost of $60 per set. At the moment the store orders headphones every 5 days resulting in a mean daily cost of $65. (a) Produce probability distribution functions for headphone sales and order arrival. Allocate random digits to these distributions. (b) The retailer is considering changing it; Jlicy every 6 days. What kind of simulation would you use 0 O Q 1:490pM9t'9' UNI-\"r?\" .. 32' (a) Produce probability distribution functions for headphone sales and order arrival. Allocate random digits to these distributions. (b) The retailer is considering changing its order policy to every 6 days. What kind of simulation wouid you use to test this policy? (:4 Use the random digits: 33426 69562 02964 36452 60762 02030 31358 45126 75246 to simulate 15 days of sales in the store given that they reorder headphones every 6 days and assuming the store has 10 speakers in stock and places an order on day 0. You may use Excel or perform the calculation by hand. You may use the following column headings to help you if you wish: Lost- - Daily End Daily Delivery 5\"\" 12:!\" Place 3:?" Ordering \""3 I I day demand amount order? coat\") \"a\" balance \"05'1\" (days) 21;\" 151 (:1) Would you recommend ordering every 6 days? Justify your answer. (a) How could your simulation be improved? (3 marks) C] 0