Chapter 5, Problem 34QP

The Tinkan Company produces one-pound cans for the Canadian salmon industry. Each year the salmon spawn during a 24-hour period and must be canned immediately. Tinkan has the following agreement with the salmon industry. The company can deliver as many cans as it chooses. Then the salmon are caught. For each can by which Tinkan falls short of the salmon industrys needs, the company pays the industry a 2 penalty. Cans cost Tinkan 1 to produce and are sold by Tinkan for 2 per can. If any cans are left over, they are returned to Tinkan and the company reimburses the industry 2 for each extra can. These extra cans are put in storage for next year. Each year a can is held in storage, a carrying cost equal to 20% of the cans production cost is incurred. It is well known that the number of salmon harvested during a year is strongly related to the number of salmon harvested the previous year. In fact, using past data, Tinkan estimates that the harvest size in year t, Ht (measured in the number of cans required), is related to the harvest size in the previous year, Ht1, by the equation Ht = Ht1et where et is normally distributed with mean 1.02 and standard deviation 0.10. Tinkan plans to use the following production strategy. For some value of x, it produces enough cans at the beginning of year t to bring its inventory up to x+Ht, where Ht is the predicted harvest size in year t. Then it delivers these cans to the salmon industry. For example, if it uses x = 100,000, the predicted harvest size is 500,000 cans, and 80,000 cans are already in inventory, then Tinkan produces and delivers 520,000 cans. Given that the harvest size for the previous year was 550,000 cans, use simulation to help Tinkan develop a production strategy that maximizes its expected profit over the next 20 years. Assume that the company begins year 1 with an initial inventory of 300,000 cans.

The Seaside Hotel is a three-star hotel in Newquay, Cornwall. It contains 108 rooms and employs 30 fulltime and 40 parttime personnel. Between May and August, the hotel's workforce is nearly doubled by casual and temporary workers. Cornwall is a difficult place to do business, especially in the tourism industry. Business is highly seasonal with hotels experiencing very low occupancy during the offseason and many hotels choose not to operate during this time. The Seaside Hotel operates all year round by supplementing its tourism trade during the off-season by offering discounted conferencing facilities for local businesses and as a cheap base for corporate events and activities, such as team building weekends. Tourism is, however, vitally important for the region and its businesses and provides a significant proportion of all jobs in the South West. Cornwall can, however, be a difficult place in which to work. For instance, Newquay – Cornwall’s most popular holiday destination – is one…

As part of a quality improvement initiative, Consolidated Electronics employees complete a three-day training program on teaming and a two-day training program on problem-solving. The manager of quality improvement has requested that at least 8 training programs on teaming and at least 10 training programs on problem-solving be offered during the next six months. In addition, senior-level management has specified that at least 25 training programs must be offered during this period. Consolidated Electronics uses a consultant to teach the training programs. During the next quarter, the consultant has 84 days of training time available. Each training program on teaming costs $10,000 and each training program on problem-solving costs $8,000.  a. Formulate a linear programming model that can be used to determine the number of training programs on teaming and the number of training programs on problem-solving that should be offered in order to minimize total cost.b. Graph the feasible…