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2008-07-03 4:35 am

1. A firm Expects its sales to grow by 12% per month. If its January sales figure is 9,200 per month what will its expected total annual sales be?

2. A developing country currently produces 3,600 million units of food per annum ad his rate of prodution is expected to increase by 4% a year. Its population is currently 2.5 million and expected to grow by 6% per annum. The minimum recommuneded average intake of food is 1,200 units of food per person per year. Assuming no changes in production or population growth rates, no imports and exports and no foreign aid, when will food production fall below the subsistence level?

回答 (1)

追求自由

2008-07-03 8:32 pm

✔ 最佳答案

1.
Sales in January: 9,200
Sales in February: 9,200 X (1+12%)
Sales in March: 9,200 X (1+12%)^2
:
Sales in December: 9,200 X (1+12%)^11

Therefore, total annual sales is
9,200 + 9,200 X (1+12%) + ...... + 9,200 X (1+12%)^11
= 9,200 X (1+1.12+1.12^2+...... +1.12^11)
= 9,200 X (1.12^12-1) / (1.12-1)
= 222,024.83

2.
Minimum food consumption at current year is 2.5 X 1,200 million units.
In the n year later, the minimum food consumption is
2.5 X 1.06^n X 1,200 million units

In the n year later, the food produced is
3,600 X 1.04^n million units

Assuming the unused food cannot be accumulated for the following years' consumption. Consider the equilibrium point,
2.5 X 1.06^n X 1,200 = 3,600 X 1.04^n
1.06^n = 1.2 X 1.04^n
n X log 1.06 = log 1.2 + n X log 1.04
n = log 1.2 / (log 1.06 - log 1.04)
= 9.57

Therefore, the food production fall below the subsistence level at the 10 years later.

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