A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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The research department at a manufacturing company has developed a new process that it believes will result in an improved product. Management must decide whether to go ahead and market the new product. The new product may or may not be better than the old one. If the new product is better and the company decides to market​ it, sales should increase by
​$60,000.
If it is not better and they replace the old product with the new product on the​ market, they will lose
​$25,000
to competitors. If they decide not to market the new​ product, they will lose a total of
​$50,000
if it is better and just research costs of
​$20,000
if it is not. Answer parts a through c below.
​(a) Prepare a payoff matrix.
 
Start 2 By 2 Table 1st Row 1st Column 60000 2nd Column negative 25000 2nd Row 1st Column negative 50000 2nd Column negative 20000 EndTable
  60000 −25000  
−50000 −20000
​(Type an integer or decimal for each matrix element. Do not include the​ $ symbol in your​ answer.)
​(b) If management believes there is a probability of
0.4
that the new product is​ better, find the expected profits under each strategy and determine the best action. Select the correct answer below and fill in the answer boxes to complete your choice.
​(Type integers or​ decimals.)
 
A.
The expected profits are
​$nothing
if they market the product and
​$nothing
if they do not. They should not market the product because they will earn more if they do not.
 
B.
The expected profits are
​$nothing
if they market the product and
​$nothing
if they do not. They should not market the product because they will lose less if they do not.
 
C.
The expected profits are
​$nothing
if they market the product and
​$nothing
if they do not. They should market the product because they will earn more if they do so.
 
D.
The expected profits are
​$nothing
if they market the product and
​$nothing
if they do not. They should market the product because they will lose less if they do.
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