Question

4.18 Jul Nov CT Gift Shop is profitable but has a cash flow problem as of the end of June. December is the busiest month, and the shop expects to make a decent profit by the end of the year. As of the end of June, the gift shop has 2,000 in cash in the bank. At the start of each month, rent and other bills are due, and the shop has to make the payments. By the end of the month the shop will receive revenues from its sales. The projected revenues and payments are as follows: Month Aug Sep Oct Dec Sales ($) 3,000 3,000 4,000 4,000 9,000 15,000 Payments ($) 6,000 5,000 8,000 3,000 4,000 6,000 CT Gift Shop has an excellent credit history and can take out loans to help cover the shortfalls. On July 1, the gift shop can take out a 6-month loan with a 10% interest rate for the period that is to be paid back at the end of December. The gift shop can also take out a 1-month loan at the start of each month at an interest rate of 2% per month. Formulate CT Gift Shop's cashflow problem as an LP so to minimize the amount of interest paid. Solve the LP by the Simplex Method.

Answer 1

	Cash Flow
	(i)	With 2% Loan Rate
	Particulatrs	Jul	Aug	Sep	Subtotal	Oct	Nov	Dec	Total
	Opening Cash	2000	0	0	2000	0	0	-0.44	1999
	Sale	3000	3000	4000	10000	4000	9000	15000	38000
	Expenses	6000	5000	8000	19000	3000	4000	6000	32000
	Interest Exp	0	20	60	80.4	142	124	27	373
	Laon Taken	1000	3020	7080	11100	6222	1346	0	18668
	Payment Of Loan	0	1000	3020	4020	7080	6222	1346	18668
	Ending Balance	0	0	0	0	0	0	7627	7626
	(ii)	With 6% Loan Rate
	Particulatrs	Jul	Aug	Sep	Subtotal	Oct	Nov	Dec	Total
	Opening Cash	2000	6000	4000	2000	0	1000	6000	19000
	Sale	3000	3000	4000	10000	4000	9000	15000	38000
	Expenses	6000	5000	8000	19000	3000	4000	6000	32000
	Interest Exp				0			700	700
	Laon Taken	7000			7000				7000
	Payment Of Loan				0			7000	7000
	Ending Balance	6000	4000	0	0	1000	6000	7300	24300

Option (i) Loan @ 2%p.m. is better option as Interest expenses in lower in that csae.

for option 2 i take 3 months cummulatice net outflow as net inflow is generating in 4th month.

do let me know in case of any doubts