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A company must meet the following demands for cash at the beginning of each of the next four months: month 1, £120; month 2, £120; month 3, £170; month 4, £110. At the beginning of month 1 the company has £254 in cash and £185 worth of bond 1, £220 worth of bond 2, and £250 worth of bond 3. The company have to sell some bonds to meet demands, but the penalty will be charged for any bonds sold before the end of month 4. The penalties for selling £1 worth of each bond are as shown in the table below. The penalties have to be paid in cash.
Bond
Month of sale
1
2
3
4
0.55
0.6
0.25
0.9
0.7
0
0.45
0.8
What is the minimal cost (i.e. the sum of all penalties paid) of meeting cash demands for the next four months? (Fractions of bonds can be sold.)
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