Jade Polish Bike makes bikes to order An order of 25 special bikes is received f
ID: 3297667 • Letter: J
Question
Jade Polish Bike makes bikes to order An order of 25 special bikes is received from Warsaw Mommy. The cost of making each bike is $55. Since the making process is highly variable, not all the bikes produced are good. Mommy Warsaw has agreed to accept 20 - 30 good bikes at the price of $140/unit. Jade, however, offers a discount of $10 unit for the sales of less than 25 units, and a 5% discount price/unit for the sales of more than 25 units. For the sales of at 25 good units to Warsaw Mommy. Jade will also provide each unit a nice gift box. For that. Jade will have an additional cost of $10/unit. Recycled value is $35/unit. All the good units that are not sold to Warsaw Mommy, however, have a recycled value of $38/unit. Jade will pay his worker $5/good unit sold to Warsaw Mommy as an incentive. His worker, on the other hand, has to pay $3/bad unit if he cannot make at least 20 good units. Please help Jade find the expected profit if he plans to make 31 bikes?Explanation / Answer
Cost of each bike = $55
Sell price of good bike = $140
If the expected good bikes are between 20 and 24
There is discount of $10
So, the Sell price of good bike = $140 - $10 = $130
Worker Incentive = $5
Cost of each bike = $55 + 5 = $60
Profit of each good bike sold = $130 - $60 = $70
Recycled value = $38
Loss of unsold bike = $55 - $38 = $17
If the expected good bikes are between 25 and 30
There is discount of 5%
So, the Sell price of good bike = $140 * 0.95 = $133
Jade will give a gift box of $10.
Worker Incentive = $5
So, now the total cost = $55 + $10 + $5 = $70
Profit of each good bike = $133 - $70 = $63
Recycled value = $38
Loss of unsold bike = $55 - $38 = $17
If the the expected good bikes are less than 20
Worker has to pay $3 per unit.
Cost of each bike = $55 - $3 = $52
Profit is 0, as the Warsaw Mommy does not accept less than 20 good bikes.
Recycled value = $38
So, the loss is $52 - $38 = $14
If there was n bikes sold, then unsold bikes = 31 - n
Let P(x = n) represents the probability that n bikes were sold.
So, the expected profit using the probabilities from the table
= P(x = 19) * 0 + P(x=20) [ Profit of sold 20 bikes - Loss of 11 unsold bikes] + P(x=21) [ Profit of sold 21 bikes - Loss of 10 unsold bikes] + P(x=22) [ Profit of sold 22 bikes - Loss of 9 unsold bikes] + P(x=23) [ Profit of sold 23 bikes - Loss of 8 unsold bikes] + P(x=24) [ Profit of sold 24 bikes - Loss of 7 unsold bikes] + P(x=25) [ Profit of sold 25 bikes - Loss of 6 unsold bikes] + P(x=26) [ Profit of sold 26 bikes - Loss of 5 unsold bikes] + P(x=27) [ Profit of sold 27 bikes - Loss of 4 unsold bikes] + P(x=28) [ Profit of sold 28 bikes - Loss of 3 unsold bikes] + P(x=29) [ Profit of sold 29 bikes - Loss of 2 unsold bikes] + P(x=30) [ Profit of sold 30 bikes - Loss of 1 unsold bikes] + P(x=31) [ Profit of sold 31 bikes]
= 0.05 *(20* 70 - 11 * 17) + 0.08 *(21* 70 - 10 * 17) + 0.08* (22* 70 - 9 * 17)+ 0.05* (23* 70 - 8 * 17)+ 0.15* (24* 70 - 7 * 17) + 0.10 *(25* 63 - 6 * 17)+ 0.10*(26* 63 - 5 * 17) + 0.08*(27* 63 - 4 * 17) + 0.06*(28* 63 - 3 * 17) + 0.10*(29* 63 - 2 * 17) + 0.10 *(30* 63 - 1 * 17)+ 0.05 * 31 * 63
= $1583.73
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