Here is a 5 by 5 assignment problem. 83 13 76 13 84 58 26 92 45 103 35 63 34 103 12 77 20 10 50 82 29 95 4 35 90 The problem is to meet the demand for minimal cost. Use the Hungarian algorithm to obtain the optimal solution and fill in your value for minimum cost:
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.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?
- Find Solution using Voggel's Approximation method, also find optimal solution using modi method D1 D2 D3 D4 Supply si 19 30 50 10 7 S2 70 30 40 60 9 S3 40 8 70 20 | 18 Demand 5 8 7 14Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimalityA company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be p = 10 − 42 D2 + 2D where p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. a) Derive how to find the number of units that should be produced annually to maximize profit. b) What is the maximum profit per year? c) What is the annual breakeven point? d) What is the company’s range of profitable output per year?
- 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 company manufactures two products. If it charges aprice pi for product i, it can sell qi units of product i, whereq1 60 3p1 p2 and q2 80 2p2 p1. It costs $25to produce a unit of product 1 and $72 to produce a unit ofproduct 2. How many units of each product should beproduced to maximize profits?Maximize Profit=123 L + 136 S 17 L+11 S≤ 3000 6 L+9 S≤2500 L20 and S20 (Availability of component A) (Availability of component B) Show Transcribed Text Implement the linear optimization model and find an optimal solution. Interpret the optimal solution. The optimal solution is to produce LaserStop models and SpeedBuster models. This solution gives the possible profit, which is $. (Type integers or decimals rounded to two decimal places as needed.)
- You are planning a vacation to Patagonia. You have a choice of 4 hotels at which to stay, and a choice of 3 different car rental companies to use. Patagonia offers 5 different day trips you can take. A vacation to Patagonia consists in selecting one hotel, one car rental company and 2 different day trips (the order doesn't matter). How many ways are there to plan your vacation? (A) 24 (B) 60 (С) 40 (D) 4 (E) 240 (F) 30 (G) 495 (Н) 120 OA OB В OD F OG OH3. A tea supplier finds that it costs $1050 to roast and package 200 pounds of tea in a day and $4850 to produce 800 pounds of tea in a day. Assume that the cost function is linear. Express the cost as a function of the number of pounds of tea they produce each day.Suppose a grocer is faced with a problem of how many cases of milk to stock to meet this week’s demand. The grocer estimates that 10, 15, 20, or 25 cases will be needed and wants to analyze the situation using a payoff table and decision theory to determine how many cases to stock. Every case of milk costs the grocer $55 and will be sold for $90 (if sold during the week). If there are cases left at the end of the week, they will be sold to a food bank for $30 per case. Fill in the payoff table (Using Excel - calculate the payoff for each combination of cases of milk ordered and cases of milk demanded). Cases demanded 10 15 20 25 Cases stocked 10 15 20 25 B. Assume the probability of demand is determined as in the table below. Demand 10 cases 15 cases 20 cases 25 cases Probability .08 .25 .45 .22 Calculate the Expected…