A small-appliance manufacturer has plants in Baltimore and Philadelphia, each of

Question

A small-appliance manufacturer has plants in Baltimore and Philadelphia, each of which produces toasters and blenders. The Baltimore plant can produce at most 800 appliances in one day at a cost of $ 12 per toaster and $15 per blender. The Philadelphia plant can produce at most 500 appliances in one day at a cost of $ 10 per toaster and $ 20 per blender. A rush order is received for 600 toaster and 300 blender. The manufacturer will choose the number of toasters and blenders produced at each plant, in order to minimize costs. What is the minimum cost? Mr. and Mrs. Adams have $ 20,000 to invest in low-risk, medium-risk and high-risk stocks. They decide that at least $ 10,000 must be invested in low-risk stocks, atleast $ 1000 must be invested in medium risk stocks and no more than $5,000 can be invested in high risk stocks. The expected yields on the stocks are 6% for low-risk, 8% for medium-risk and 10% for high-risk. Mr. and Mrs. Adams will choose the amount to invest in each type of stock in order to maximize the yield on their investment What amount should they invest in each type of stock? what is their maximum yield?

Explanation / Answer

Solution: The total amount is $20000. So now lets start with the high risk stocks.

Maximum money that can be invested ( because it yields more than the other two's) = $5000

So after investing total yield = 5000 x 1.10 = $5500

Now come to medium risk .

Now the money left is $15000 and $10000 is the minimum amount that shoud be invested in low risk. So they can invest $5000 in medium risk profile.

Total yield = $5000 x 1.08 = $5400

Now the low risk stocks.

Total money to invest = $10000

Total yield = 10000 x 1.06 = $10600

So total maximum yield = $5500 + $5400 + $10600 = $21500.

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