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Short Probability Question

A manufacturer makes two products. The manufacturing plant has a capacity to produce a total of 100 units per week, in any combination of  these two products i.e. It can make X units of product A and 100-X units of  product B (whereas, value of X can be from 0 to 100). It costs $20 per unit to make product A, and it sells for $30. Whatever amount of Product A is made, it is sold immediately. Product B costs $10 per unit to make, and sells for $100, but demand is uncertain. Product B is produced in batches once a week. Any unsold unit of Product B has no salvage value. The probability distribution of demand for Product B is shown below. How many units of both products should be produced and what will be total (expected) profit 

from both products?


Demand     5,6,7,8,9,10

Probability 0.10, 0.20, 0.25, 0.20, 0.20, 0.05

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