2. The Warwick Manufacturing Company produces shovels for industrial and home use. Sales of the shovels are seasonal, and Warwick’s customers refuse to stockpile themduring slack periods. In other words, the customers want to minimize inventory, insist on shipments according to their schedules, and will not accept backorders. Warwick employs manual, unskilled laborers, who require only very basic training. Producing 1,000 shovels costs $3,500 on regular time and $3,700 on overtime. These amounts include materials, which account for over 85 percent of the cost.Overtime is limited to production of 15,000 shovels per quarter. In addition, subcontractors can be hired at $4,200 per thousand shovels, but Warwick’s labor contract restricts this type of production to 5,000 shovels per quarter. The current level of inventory is 30,000 shovels, and management wants to end the year at that level. Holding 1,000 shovels in inventory costs $280 per quarter. Thelatest annual demand forecast is
Build a linear programming model to determine the best regular-time capacity plan. Assume that : • the firm has 30 workers now, and management wants to have the same number in quarter 4. • each worker can produce 4,000 shovels per quarter. • hiring a worker costs $1,000, and laying off a worker costs $600. 3) The United Shipping Company has three hubs, located inDetroit (D), Houston (H) and Boston (B), that handle shipments in pallets with uniform size, shape and weight. The hubs serve five major customers in Atlanta (A), Rochester (R), Pittsburg (P), Utah (U), and San Francisco (SF). To ease pressure on its existing hubs and also to have a presence in the Southwest, United is considering the addition of one more hub with a capacity of 40 pallets in one ofthree cities: Phoenix (Ph), Los Angeles (LA), or Las Vegas (LV). The table below shows the transportation cost per pallet from each hub (existing as well as proposed) to each customer area as well as variable operacional cost (per pallet) at each existing and proposed hub. Determine where the new hub should be built to minimize operacional costs at the hub and distribution costs between hubs andcustomer areas. a) Use a single mathematical optimizacion model to choose the optimal strategy.
Transportation Costs to Customer Location Areas per Pallet A R P U SF D 17 11 11 30 55 H 9 12 10 15 40 B 17 6 9 23 42 Ph 28 35 30 13 13 LA 55 52 44 9 4 LV 45 50 44 8 5 Demand 35 20 20 18 40
Handling Capacity Cost 50 20 25 40 40 40 2.7 2.7 3.0 1.5 2.9 2.0
b) Suppose the Location B wants to expandits capacity considering the following possibilities:
Quantity to be expanded 5 10 15 -
Cost of the expansion ($/ton) 34 24 14
Improve the model including all the elements you need to determine which expanded capacity is the best.
5) formular y resolver utilizando winqsb, el problema de gasahol inc. que se encuentra en las paginas 114 y 115 del libro de mathur y solow(investigación de operaciones).
6) The law ﬁrm of Mason and Burger employs three types of lawyers: junior lawyers, senior lawyers, and partners. During a given year, there is a .15 probability that a junior lawyer will be promoted to senior lawyer and a .05 probability that he or she will leave the ﬁrm. Also, there is a .20 probability that a senior lawyer will be promoted to partner and a .10probability that he or she will leave the ﬁrm. There is a .05 probability that a partner will leave the ﬁrm. The ﬁrm never demotes a lawyer. There are many interesting questions the law ﬁrm might want to answer.
Junior Senior Partner Leave as NP Leave as P
A) What is the average length of time that a newly hired junior lawyer spends working for the ﬁrm? B) What is the probability that a junior...