Problem#3A large bakery buys flour in 25-pound bags. The bakery uses an average of' 4,860 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $10 per order. Annual carrying costs are $75 per bag. (A) Determine the economic order quantity. (B) What is the average number of bags on hand? (C) How many orders per year will there be? (D) Compute the total cost of ordering and carrying flour. (E) If ordering costs were to increase by $1 per order, how much that would affect the minimum total annual cost? ANSWER D = 4,860 bags/yr. S = $10 H = $75 2DS 2(4,860)10 = = 36 bags H 75 b. Q/2 = 36/2 = 18 bags a. Q = c. D 4,860 bags = =135 orders Q 36 bags / orders D d. TC = Q / 2H + Q S = 36 4,860 (75) + (10) = 1,350 +1,350 = $2,700 2 36 e. Using S = $5, Q = TC = 2( 4,860)(11) = 37.757 75 37.757 4,860 (75) + (11) =1,415.89 +1,415.90 = $2,831.79 2 37.757 Increase by [$2,831.79 – $2,700] = $131.79 Problem#9 The friendly Sausage factory (FSF) can produce hot dogs at a rate of 5,000 units per day. FSF supplied hot dogs to local restaurant at a steady state rate of 250 per day. The cost to prepare equipment for producing hot dog is $66. Annual holding cost is 45 cents per hot dog. The factory operates 300 days a year. Find a) The optimal run size. b) The number of runs per year. c) The length (in days) of a run. 2 TC = I max D H+ S 2 Q TCorig. c. Q0 = 2DS H p = p −u b.000)100 5 50 = 516. 200 days/yr. Run length = Q 516. 6.549. The firm operates 200 days a year. I max = 2( 4.812 = 15. 300 days per year S = $66 H = $.8 bags] P 50 Average is I max 309.75 [approx. = 75.328 bags] 50 − 20 Q 516.00 .000 tons/yr.40 tons [10.45/hotdog per yr. a.59. = 4. Demand for this product is 20 tons per day. or approximately 1 day Problem#10 A chemical firm produces sodium bisulphate in 100-pound bags.000 hotdogs/day u = 250 hotdogs/day D= 250/day x 300 days/yr. a.84 tons [approx.812] 4. The capacity for producing the product is 50 tons per day.4 = =10.098 bags] 2 2 c.92 tons [approx. Setup cost $100 and storage and handling cost are $5 per ton a year.4 (p − u ) = (30) = 309.000 d. Runs per year: Q = 516.000 hotdogs/yr. D/Qo = 75.000/4.000 = . 3. or about 16 runs/yr.96 days.000)66 .27 [round to 4.4 = 7. Run length: Qo/p = 4.ANSWER p = 5.196. Q0 = 2DS H p = p −u 2(75. S = $100 H = $5/ton per yr.48 : = 154.000 = 4.812/5. (Note 1 ton = 2000 pounds) a) How many bags per run are optimal? b) What would the average inventory be for this lot size? c) Determine the approximate length of a production run in days? d) About how many runs per year would there be? e) How much could the company save annually if the setup cost reduced to $25 per run? ANSWER p = 50/ton/day u = 20 tons/day D= 20 tons/day x 200 days/yr. Q′ = 258. 8] e. = $1.33 days P 50 D 4.812.750 b.45 5. TCrev. .50 Thus.50. savings would be $774. = $ 774.