Concept explainers
a)
To determine: The way the company can maximize the profit.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
b)
To determine: The way the optimal solution changes as the price of gasoline varies from $65-$85 per each barrel.
Linear programming:
It is a mathematical modeling procedure where a linear function is maximized or minimized subject to certain constraints. This method is widely useful in making a quantitative analysis which is essential for making important business decisions.
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Chapter 4 Solutions
Practical Management Science
- 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.arrow_forwardIn the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?arrow_forwardSeas Beginning sells clothing by mail order. An important question is when to strike a customer from the companys mailing list. At present, the company strikes a customer from its mailing list if a customer fails to order from six consecutive catalogs. The company wants to know whether striking a customer from its list after a customer fails to order from four consecutive catalogs results in a higher profit per customer. The following data are available: If a customer placed an order the last time she received a catalog, then there is a 20% chance she will order from the next catalog. If a customer last placed an order one catalog ago, there is a 16% chance she will order from the next catalog she receives. If a customer last placed an order two catalogs ago, there is a 12% chance she will order from the next catalog she receives. If a customer last placed an order three catalogs ago, there is an 8% chance she will order from the next catalog she receives. If a customer last placed an order four catalogs ago, there is a 4% chance she will order from the next catalog she receives. If a customer last placed an order five catalogs ago, there is a 2% chance she will order from the next catalog she receives. It costs 2 to send a catalog, and the average profit per order is 30. Assume a customer has just placed an order. To maximize expected profit per customer, would Seas Beginning make more money canceling such a customer after six nonorders or four nonorders?arrow_forward
- Formulate and then solve a linear programming model of this problem, to determine how manycontainers of each product to produce tomorrow to maximize profits. The company makes fourjuice products using orange, grapefruit, and pineapple juice.Product Retail Price per QuartOrange juice $1.00Grapefruit juice .90Pineapple juice .80All-in-One 1.10The All-in-One juice has equal parts of orange, grapefruit, and pineapple juice. Each product isproduced in a one-quart size (there are four quarts in a gallon). On hand are 400 gallons of orangejuice, 300 gallons of grapefruit juice, and 200 gallons of pineapple juice. The cost per gallon is$2.00 for orange juice, $1.60 for grapefruit juice, and $1.40 for pineapple juice.In addition, the manager wants grapefruit juice to be used for no more than 30 percent of thenumber of containers produced. She wants the ratio of the number of containers of orange juice tothe number of containers of pineapple juice to be at least 7 to 5.arrow_forwardProducts A,B, and C are sold door-to-door. A costs $ 3 per unit, take 10 minutes to sell (on the average) and costs $0.50 to deliver to customer. B costs $ 5, takes 15 minutes to sell, and is left with the customer at the time of sale. C costs $ 4, takes 12 minutes to sell, and costs $ 1 to deliver. During any week, a salesperson is allowed to draw up to $ 500 worth of A,B,C (at cost) and is allowed delivery expenses not to exceeds $ 75. If a salesperson’s selling time is not expected to exceed 30 hours (1,800 minutes) in a week, and if the salesperson profit (net after all expenses) is $ 1 each on a unit of A and B and $ 2 on a unit of C, what combination of sales of A, B, and C will lead to maximum profit, and what is the maximum profIt?arrow_forwardYou are a Business Analyst working for the ABC Ball Bearing company. An hour ago, you sent an order of 74 boxes of your A1 ball bearings to a customer on your delivery truck. You have just found out that your truck is going to go over a bridge that has a weight limit of 11,500 lbs. You need to determine if your truck will safely make it over the bridge. If you determine that the truck cannot make it over the bridge, you will need to call the driver and have him/her turn back. The plant manager has told you that an empty delivery truck with the driver weights about 8500 lbs. You have 30 boxes of the A1 ball bearings in your plant. You immediately had them weighed. The weights of the boxes are: 40.1 41.1 39.5 40.1 39.1 41.2 37.6 39.1 41.6 40.8 43.2 38.9 38.1 43.5 36.9 39.1 40.5 41.2 37.6 44.0 38.0 39.8 42.1 38.6 41.3 43.7 36.9 43.6 38.1 40.2 1. Discuss what sampling bias is. Do you believe that using the 30 boxes in your warehouse caused sampling…arrow_forward
- Why is the RISKCORRMAT function necessary?How does @RISK generate random inputs by default,that is, when RISKCORRMAT is not used?arrow_forwardCWD Electronics sells Televisions (TV), which it orders from the USA. Because of shipping and handling costs, each order must be for 10 TVs. Because of the time it takes to receive an order, the company places an order every time the present stock drops to 5 TVs. It costs $50 to place an order. It costs the company $200 in lost sales when a customer asks for a TV and the warchouse is out of stock. It costs $50 to keep each TV stored in the warehouse. If a customer cannot purchase a TV when it is requested, the customer will not wait until one comes in but will go to a competitor. The following probability distribution for demand for TV has been and the time required to recæive an order once it is placed (lead time) has the following probability distribution: Lead time (weeks) Probability Demand/ week Probability 0.45 0.15 2 0.30 025 0.25 3 0.40 020 The company has 10 TVs in stock. Orders are always received at the beginning of the week. Note that a lead time of 2 weeks imply that an…arrow_forwardLong-Life Insurance has developed a linear model that it uses to determine the amount of term life Insurance a family of four should have, based on the current age of the head of the household. The equation is: y=150 -0.10x where y= Insurance needed ($000) x = Current age of head of household b. Use the equation to determine the amount of term life Insurance to recommend for a family of four of the head of the household is 40 years old. (Round your answer to 2 decimal places.) Amount of term life insurance thousandsarrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,