Question

A firm designs and manufactures automatic electronic control devices that are installed at customers' plant sites. The control devices are shipped by truck to customers' sites; while in transit, the devices sometimes get out of alignment. More specifically, a device has a prior probability of 10 of getting out of alignment during shipment. When a control device is delivered to the customer's plant site, the customer can install the device. If the customer installs the device, and if the device is in alignment, the manufacturer of the control device will realize a profit of $16,000. If the customer installs the device, and if the device is out of alignment, the manufacturer must dismantle, realign, and reinstall the device for the customer. This procedure costs $3,200, and therefore the manufacturer will realize a profit of $12,800. As an alternative to customer installation, the manufacturer can send two engineers to the customer's plant site to check the alignment of the control device, to realign the device if necessary before installation, and to supervise the installation. Since it is less costly to realign the device before it is installed, sending the engineers costs $600. Therefore, if the engineers are sent to assist with the installation, the manufacturer realizes a profit of $15,400 (this is true whether or not the engineers must realign the device at the site). Before a control device is installed, a piece of test equipment can be used by the customer to check the device's alignment. The test equipment has two readings, "in" or "out" of alignment. If the control device is in alignment, there is a 0.7 probability that the test equipment will read "in." If the control device is out of alignment, there is a 0.8 probability that the test equipment will read "out." Carry out a posterior analysis of the control device problem. That is, decide whether the engineers should be sent, and find the expected monetary value associated with either sending or not sending (depending on which is best) the engineers assuming: (a) The test equipment "reads in." (Round intermediate calculations to 4 decimal places and final answers to the nearest whole number.) Test equipment "reads in": EMV(Not Send) EMV(Send) Choose: engineers

Answer 1

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If 15 Ans: - Given, customer installs the device & reads in then Profit $16000 If customer installs the device ļ it goes out of alignment then manufacturer must dismentle, realign and reinstall the device for customer & this cost $3.200. Then profit is $12800 ile $16000-3200 $12800 & If manufactures sent two engineer then. sending engêncer cost $600 for realign the device then profit is $15400. if device is read in $15400 + $600 $ 16000 Given, prob. for read in and out alignment is 0.7 & 0.8 respectively Payoff table; Read in Read out Prob. So, 0.7 Engineer Not send $ 16000 $12800 $15400 $15400 send a> Test equipment reads in': EMV CNot send) 0.7x $16000 EMV (Not send = $ 11,200 EMV (send) = 0.7* $15400 EMV (send) = $10,780

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b) Test equipment reads out' : EMV (not send) = 0.8 * $12800 = $10240. EMV (send) = 0.88 $15400 = $12320 from EMV table; All calculated Emu's represent or written in one table below, EMV Reads in Reads out not send $11208 $10240 send $10780 $ 2320 bo