Hi, pls help on the below question. Thanks.
Assume that it is the first of July and you are running a small shop. The sales revenue and the amount of bills you have to pay for the next six months are estimated as following:
Month Sales Revenue ($) Bills ($)
July 3,000 6,000
August 2,000 6,000
September 1,000 4,000
October 2,000 2,000
November 6,000 1,000
December 10,000 1,000
Half Year total 24,000 20,000
In short, you will make $4,000 profit at the end of the year. However, since all bills must be paid in full every month, you may be short on cash in earlier months until you see the big sales in November and December. You have two sources of loan:
- Long term loan of six months at 10% of interest, example, you borrow $100 now, and payback $110 at the end of the year. Early-pay-back is not allowed. You have to keep the money for six months at 10% of interest.
- Monthly loan at 4% of interest, example you borrow $100 at the beginning of any month and pay back $104 at the end of the month. No monthly loan is available in December.
Assume that you have zero cash at the moment.
Apply the linear programming to find the loan plan to minimise the interest payment. Formulate the problem as a linear programme and state assumptions you have made in your formulation.
Assume that it is the first of July and you are running a small shop. The sales revenue and the amount of bills you have to pay for the next six months are estimated as following:
Month Sales Revenue ($) Bills ($)
July 3,000 6,000
August 2,000 6,000
September 1,000 4,000
October 2,000 2,000
November 6,000 1,000
December 10,000 1,000
Half Year total 24,000 20,000
In short, you will make $4,000 profit at the end of the year. However, since all bills must be paid in full every month, you may be short on cash in earlier months until you see the big sales in November and December. You have two sources of loan:
- Long term loan of six months at 10% of interest, example, you borrow $100 now, and payback $110 at the end of the year. Early-pay-back is not allowed. You have to keep the money for six months at 10% of interest.
- Monthly loan at 4% of interest, example you borrow $100 at the beginning of any month and pay back $104 at the end of the month. No monthly loan is available in December.
Assume that you have zero cash at the moment.
Apply the linear programming to find the loan plan to minimise the interest payment. Formulate the problem as a linear programme and state assumptions you have made in your formulation.