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Ber [7]
3 years ago
14

Adirondack Savings Bank (ASB) has $5 million in new funds that must be allocated to home loans, personal loans, and automobile l

oans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.(a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds.(b) How much (in dollars) should be allocated to each type of loan? 1) What is the total annual return (in dollars)?2) What is the annual percentage return?
Mathematics
1 answer:
Vesna [10]3 years ago
5 0
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If I read the question correctly, the information about the 80x80 fencing and the grass region are all irrelevant information. 

In order to find the area of the side walk we are going to use the formula A=pi(r^2) where r = the radius. The diameter of the pool is 60 feet and the the sidewalk is 5 feet bigger all around meaning we had 5 feet to both sides of this 60 feet giving you an overall diameter of 70 feet (or 60 + 5*2). To find the radius take half of the diameter. 70/2 = 35. 

Now we plug in 35 to the equation. A = Pi(35^2) = 1225pi. Leave your answer like this as we are not finished and will need to round at the end for an accurate answer. This is NOT the end, that number is the area of the sidewalk AND the pool.

The sidewalk is not a full circle, just a border so we now have to find the area of the actual pool and subtract it from this 1225pi for the sidewalk's area. Same formula, Area = pi(r^2). The diameter of the pool is 60 meaning the radius is 30 (or 60/2). Plug into the equation, pi(30^2) = 900pi.

Now do 1225pi - 900pi to get 325pi. Break out your calculator and hit the approximation button. 325pi is approximately 1021.018 if rounded to 3 decimal places.

The area of the 5-foot wide sidewalk encircling the pool is approximately 1021.018 square feet. 


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