Compute the expected profit for each of the expansion plans. A shoe producer mak
ID: 3316562 • Letter: C
Question
Compute the expected profit for each of the expansion plans.
A shoe producer makes a variety of footwear, including indoor slippers, children's shoes, and flip-flops. To keep up with increasing demand, it is considering three expansion plans:
(1) a small factory with yearly costs of $150,000 that will increase the production of flip-flops by 400,000 ;
(2) a mid-sized factory with yearly costs of $250,000 that will increase the production of flip-flops by 600,000; and
(3) a large factory with yearly costs of $350,000 that will increase the production of flip-flops by 900,000.
The profit per flip-flop is projected to be $0.75. The probability distribution of the increased demand for flip-flops is provided. Let x represent the amount of profit the producer will make.
Compute the expected profit for each of the expansion plans.
Small Plan E(x)equals=
Mid-Sized Plan E(x)equals=
Large Plan E(x)equals=
x P(x) 350,000 0.3 750,000 0.5 900,000 0.2Explanation / Answer
The current demand figures are not given, so we can assume that the values of X given in the probability table correspond to the additional demand over the current demand .
The demand is 350,000 with probability 0.3, 750,000 with probability 0.5 and 900,000 with probability 0.2. For a small plant, the production is limited to 400,000. So although the demand would be 750,000 with probability 0.5 and 900,000 with probability 0.2, the sales would be limited to 400,000. Similarly for a mid-sized plant, the sales would be limited to 600,000
A. Profit from the small plant = 0.3x(350,000x0.75) +0.5x (400,000x0.75) + 0.2 x (400000x0.75) - 1,50,000= 78,750+150,000-1,50,000=$138,750
B. Profit from the mid-sized plant = 0.3x350,000x0.75 +0.5x600,000x0.75+ 0.2 x (600000x0.75)-250,000= 78,750+225,000+90000-250,000=$143,750
C. Profit from the large plant = 0.3x350,000x0.75+ 0.5x750,000x0.75+0.2x900,000.x 0. 75 - 350,000=78,750+ 281,250+135,000-350,000=$145,750
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