Write the objective function and he constraints Diagram the constraint and identify the feasible region Using the corner point method, identify the production level that meets the objective of maximum profit
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- A manufacturer produces two types of calculator; each requiring material and labour as shown below:
Input |
Scientific Calculator |
Graphic Calculator |
Availability |
Labour (hrs) |
4 |
5 |
200 |
Inspection time |
2 |
1 |
80 |
Material (cm2) |
10 |
12 |
600 |
PROFIT |
$200 |
$300 |
|
- Write the objective function and he constraints
- Diagram the constraint and identify the feasible region
- Using the corner point method, identify the production level that meets the objective of maximum profit
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- 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.Lemingtons is trying to determine how many Jean Hudson dresses to order for the spring season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100. The contract between Jean Hudson and Lemingtons works as follows. At the beginning of the season, Lemingtons reserves x units of capacity. Lemingtons must take delivery for at least 0.8x dresses and can, if desired, take delivery on up to x dresses. Each dress sells for 160 and Hudson charges 50 per dress. If Lemingtons does not take delivery on all x dresses, it owes Hudson a 5 penalty for each unit of reserved capacity that is unused. For example, if Lemingtons orders 450 dresses and demand is for 400 dresses, Lemingtons will receive 400 dresses and owe Jean 400(50) + 50(5). How many units of capacity should Lemingtons reserve to maximize its expected profit?1. Explain the meaning of the expected value of perfect information (EVPI) in this problem. Based on the results of (iii) and (iv), which investment would you choose? 2. Compute the coefficient of variation, the return-to-risk ratio (RTRR) for each investment. Based on (vii) and (viii), what investment would you choose? Compare the results of (vi) and (ix) and explain any differences
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- Consider the following profit matrix O Oz 02 0, 04 30 23 10 -3 a2 15 27 20 19 az 13 17 29 32 18 a4 31 21 13 No probabilities are known for the occurrence of the nature states. Compare the solutions obtained by each of the following criteria: а. Laplace b. Махіmin(Minimax) c. Savage d. Hurwitz (assume that a = 0.5)A bakery must decide how many pies to prepare for the upcoming weekend. The bakery has the option to make 50, 100, or 150 pies. Assume that demand for the pies can be 50, 100, or 150. Each pie costs $5 to make and sells for $7. Unsold pies are donated to a nearby charity center. Assume that there is no opportunity cost for lost sales. Refer to the information above. Assume that the bakery has obtained the following probability information regarding demand for the pies: P(50) = 0.3, P(100) = 0.5, and P(150) = 0.2. What is the expected value under certainty? Question 5 options: 0 190 280 902. Zara is determining how many coats to order for this upcoming winter selling season. Zara forecasts the demand distribution for coats this upcoming winter to be the following. Demand (number of coats) Probability 100 0.2 150 0.1 200 0.2 250 0.1 0.1 0.3 300 350 Each coat costs Zara $100 to purchase wholesale and sells for $200 retail. At the end of the winter selling season, Zara may sell as many coats as it desires at a salvage value of $50 per coat. a. Suppose that Zara has purchased 250 coats, what is the marginal value from a 251st coat? Is it profitable for Zara to purchase its 251st coat? Justify your answer. b. Suppose that Zara has purchased 260 coats, what is the marginal value from a 261st coat? Is it profitable for Zara to purchase its 261st coat? Justify your answer. c. What is the optimal number of coats for Zara to purchase in order to maximize its average profit?
- The Fish House (TFH) in Norfolk, Virginia, sells fresh fish and seafood. TFH receives daily shipments of farm-raised trout from a nearby supplier. Each trout costs $2.45 and is sold for $3.95. To maintain its reputation for freshness, at the end of the day TFH sells any leftover trout to a local pet food manufacturer for $1.25 each. The owner of TFH wants to determine how many trout to order each day. Historically, the daily demand for trout is: Demand 10 11 12 13 14 15 16 17 18 19 20 Probability 0.02 0.06 0.09 0.11 0.13 0.15 0.18 0.11 0.07 0.05 0.03 a. Construct a payoff matrix for this problem. b. How much should the owner of TFH be willing to pay to obtain a demand forecast that is 100% accurate? give a clear explanation for (b)Problem 2 Suppose that for years East Campus' short-run Phillips Curve was such that each 1 percentage point increase in its unemployment rate was associated with a 2-percentage point decline in its inflation rate. Then, during several recent years, the short-run pattern changed such that its inflation rate rose by 3 percentage points for every 1 percentage point drop in its unemployment rate. Graphically, did East Campus' Phillips Curve shift upward or did it shift downward?Please calculate the price elasticity of demand for this pair of headphones under the following conditions (please include each step for the calculation): When the price of this pair of headphones is $150, it can sell 500 pairs. When the price drops to $100, it can sell 1,000 pair.