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- Grey Manufacturing Company expects sales to total 13,000 units in the first quarter, 12,000 units inthe second quarter, and 15,000 units in the third quarter of the current fiscal year. Company policyis to have on hand at the end of each quarter an amount of inventory equal to 10% of the followingquarter’s sales. Given this information, how many units should be scheduled for production in thesecond quarter?A firm has revenue function given by R=10Q where R=Gross Revenue and Q=Numberof Units Sold, Production Cost function is given byC = 20000+ 50(Q/800)^2Find:(i) the total Profit function, and(ii) the number of Units (Q) to be sold to get the maximum ProfitA warehouse has an end-of-period capacity of 3 units.During a period in which production takes place, a setupcost of $4 is incurred. A $1 holding cost is assessed against each unit of a period’s ending inventory. Also, a variableproduction cost of $1 per unit is incurred. During eachperiod, demand is equally likely to be 1 or 2 units. Alldemand must be met on time, and b .8. The goal is tominimize expected discounted costs over an infinite horizon. a Use the policy iteration method to determine an op-timal stationary policy. b Use linear programming to determine an optimalstationary policy.c Perform two iterations of value iteration.
- A warehouse can store up to 100 units of a particular item. In each of the next N days weneed to determine the number of units to sell and then the number of units to buy. Sellingin each day precedes buying so that the maximum amount that can be sold is the initialinventory at the beginning of the day. The maximum amount that can be bought is limitedby the capacity minus the amount in inventory after selling takes place. Inventory can beheld overnight in the warehouse, provided the total number of units held does not exceed thewarehouse capacity. At the beginning of day 1, before selling takes place, there are 40 unitsof inventory in the warehouse. Suppose that pnand cnare the per unit selling and buyingprices, respectively, for each day n = 1, . . . , N . Formulate an LP in general form to determinethe amount to be sold and bought each day to maximize total profit. Make sure you havedefined your variables clearly. PLEASE provide steps on how you solved so I understand why the answer…Suppose that because of air pollution concerns, Jansen might have to lower the Reid vapor pressure maximum on each gas type (by the same amount). Use SolverTable to explore how such a change would affect Jansen’s optimal revenueProduction and Materials Purchases Budgets White Corporation’s budget calls for the following sales for next year:Quarter 1 90,000 units Quarter 3 68,000 unitsQuarter 2 76,000 units Quarter 4 96,000 unitsEach unit of the product requires 3 pounds of direct materials. The company’s policy is to begineach quarter with an inventory of product equal to 5% of that quarter’s estimated sales requirementsand an inventory of direct materials equal to 20% of that quarter’s estimated direct materials requirements for production.Required Determine the production and materials purchases budgets for the second quarter.
- An optometrist orders eyeglass frames at a cost of $40per frame and sells each frame for $70. Annual holding costis 20% of the optometrist’s cost of purchasing a frame. Eachtime frames are ordered, a cost of $200 is incurred. Becauseof lost goodwill, a cost of $50 is incurred each time acustomer wants a frame that is not in stock. Frames aredelivered one week after an order is placed. Annual demandfor frames is N(1,040, 15.73).a Assuming all shortages are backlogged, determinethe order quantity and reorder point. b Assuming all shortages result in lost sales, deter-mine the order quantity and reorder point. c To meet 95% of all orders from stock, what shouldbe the reorder point?d To have shortages occur during an average of twolead times per year, what should be the reorder point?[item no. 9] In marginal analysis with discrete distributions for single-period inventory models, the value of ML/(ML+MP) is 0.8. The probability distribution of sales is given by the following by the table below. Find the optimal number of units to order. Daily demand 80 90 100 110 120 Probability that demand will be at this level 0.10 0.20 0.30 0.30 0.10 a. 90 units b. 110 units c. 100 units d. 80 unitsTwo plants supply three customers with medicalsupplies. The unit costs of shipping from the plants to thecustomers, along with the supplies and demands, are givenin Table 42. TAB LE 42ToFrom Customer 1 Customer 2 Customer 3 SupplyPlant 1 $55 $65 $80 35Plant 2 $10 $15 $25 50Demand 10 10 10 a The company’s goal is to minimize the cost of meeting customers’ demands. Find two optimal bfs for thistransportation problem.b Suppose that customer 2’s demand increased by oneunit. By how much would costs increase?
- A retired couple supplement their income by making fruit pies, which they sell to a local grocery store. During the month of September, they produce apple and grape pies. The apple pies are sold for $10.00 to the grocer, and the grape pies are sold for $8.00. The couple is able to sell all of the pies they produce owing to their high quality. They use fresh ingredients. Flour and sugar are purchased once each month. For the month of September, they have 1,500 cups of sugar and 2,400 cups of flour. Each apple pie requires 1½ cups of sugar and 3 cups of flour, and each grape pie requires 2 cups of sugar and 3 cups of flour. a. Determine the number of grape and the number of apple pies that will maximize revenues if the couple working together can make an apple pie in 6 minutes and a grape pie in 3 minutes. They plan to work no more than 60 hours. (Round your answers to nearest whole number.) b. Determine the amounts of sugar, flour, and time that will be unused. (Leave no cells blank -…You are given a linear programming problem. Maximize P = 6x + 4y subject to 2x + 3y ≤ 12 Resource 1 2x + y ≤ 8 Resource 2 y ≥ 0 x ≥ 0 (a) Use the method of corners to solve the problem. The maximum is P = at (x, y) = . (b) Suppose P = cx + 4y. Find the range of values that the coefficient c of x can assume without changing the optimal solution. ≤ c ≤ (c) Find the range of values that Resource 1 can assume. ≤ (Resource 1) ≤ (d) Find the shadow price for Resource 1.(e) Identify the binding and nonbinding constraints. constraint 1 constraint 2Please do not give solution in image formate thanku. 3. Kings Department Store has 625 rubies, 800 diamonds, and 700 emeralds from which they will make bracelets and necklaces that they have advertised in their Christmas brochure. Each of the rubies is approximately the same size and shape as the diamonds and the emeralds. Kings will net a profit of $250 on each bracelet, which is made with 2 rubies, 3 diamonds, and 4 emeralds, and $500 on each necklace, which includes 5 rubies, 7 diamonds, and 3 emeralds. Formulate as an LP problem to maximize profit?