MLS has P3,000 in external funds available to cover the expenses of this operation. The needed additional funds will be generated externally from a local bank that has offered a line of short-term credit in an amount not to exceed P10,000. The interest rate over the life of the loan will be 12% per year on the average amount borrowed. One stipulation set by the bank requires that the total of the MLS cash allocated to this operation plus the accounts receivable for this product line must be at least twice as great as the outstanding loan plus interest at the end of the initial production period. In addition, the man-hour capacity of MLS is only 2,500 hours of assembly time and 150 hours of packaging and shipping time available for the new product line during the initial three-month production period. The other cost, price and production time requirements for the two models of bag are shown below. Model Materials & other variable Bagi Baga expenses (unit cost P) 50 100 Selling Profit price (P) margin (P) 58 120 8 20 Assembly dept. (man-hours) 12 25 Packaging & shipping (man-hours) 1 2 Additional restrictions that were imposed by MLS management in order to guarantee that the market reaction to both models of bag can be tested is that; at least 50 units of model 1 (bag 1) and at least 25 units of model 2 (bag 2) must be produced in this initial production period. Since the cost of units produced on borrowed funds will in effect experience an interest charge, the profit margins for the units of models 1 and 2 produced on borrowed funds will be reduced. Hence, there will be 4 decision variables for this problem. Assume that all units of each model are sold as they are produced to independent distributors and that the average rate of turnover of accounts receivable is three months. The funds borrowed to produce one unit of model 1 or 2 will be repaid approximately three months later; that is, (Php50 z 12X¹) and (Php100 x 12X¹). (a) Give the decision variables (Hint: 4 decision variables) (b) Formulate the complete linear programming model
MLS has P3,000 in external funds available to cover the expenses of this operation. The needed additional funds will be generated externally from a local bank that has offered a line of short-term credit in an amount not to exceed P10,000. The interest rate over the life of the loan will be 12% per year on the average amount borrowed. One stipulation set by the bank requires that the total of the MLS cash allocated to this operation plus the accounts receivable for this product line must be at least twice as great as the outstanding loan plus interest at the end of the initial production period. In addition, the man-hour capacity of MLS is only 2,500 hours of assembly time and 150 hours of packaging and shipping time available for the new product line during the initial three-month production period. The other cost, price and production time requirements for the two models of bag are shown below. Model Materials & other variable Bagi Baga expenses (unit cost P) 50 100 Selling Profit price (P) margin (P) 58 120 8 20 Assembly dept. (man-hours) 12 25 Packaging & shipping (man-hours) 1 2 Additional restrictions that were imposed by MLS management in order to guarantee that the market reaction to both models of bag can be tested is that; at least 50 units of model 1 (bag 1) and at least 25 units of model 2 (bag 2) must be produced in this initial production period. Since the cost of units produced on borrowed funds will in effect experience an interest charge, the profit margins for the units of models 1 and 2 produced on borrowed funds will be reduced. Hence, there will be 4 decision variables for this problem. Assume that all units of each model are sold as they are produced to independent distributors and that the average rate of turnover of accounts receivable is three months. The funds borrowed to produce one unit of model 1 or 2 will be repaid approximately three months later; that is, (Php50 z 12X¹) and (Php100 x 12X¹). (a) Give the decision variables (Hint: 4 decision variables) (b) Formulate the complete linear programming model
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. In Los Baos, Laguna, the use of plastic bags and any plastic materials were prohibited
to eliminate the dangerous effects of plastics to humans and the environment. In
cooperation with the local government, the Makiling Likhang Sining (MLS), which
produces environment-friendly bags, will begin production of two newly developed bags
during the next three (3) months. MLS will need operating funds to cover the material
cost, labor, and selling expenses during this initial production period. Income from
this initial production operation will not be available until after the end of the period;
thus, MLS must arrange to finance for these operating expenses before production can
begin.
MLS has P3,000 in external funds available to cover the expenses of this operation.
The needed additional funds will be generated externally from a local bank that has
offered a line of short-term credit in an amount not to exceed P10,000. The interest.
rate over the life of the loan will be 12% per year on the average amount borrowed. One
stipulation set by the bank requires that the total of the MLS cash allocated to this
operation plus the accounts receivable for this product line must be at least twice as
great as the outstanding loan plus interest at the end of the initial production period.
In addition, the man-hour capacity of MLS is only 2,500 hours of assembly time and
150 hours of packaging and shipping time available for the new product line during
the initial three-month production period. The other cost, price and production time
requirements for the two models of bag are shown below.
Model
Bagi
Bag2
Materials &
other variable
expenses
(unit cost P)
50
100
Selling
price (P)
58
120
Profit
margin (P)
8
20
Assembly
dept.
(man-hours) (man-hours)
Packaging &
shipping
12
25
1
2
Additional restrictions that were imposed by MLS management in order to guarantee
that the market reaction to both models of bag can be tested is that; at least 50 units
of model 1 (bag 1) and at least 25 units of model 2 (bag 2) must be produced in this
initial production period.
Since the cost of units produced on borrowed funds will in effect experience an interest
charge, the profit margins for the units of models 1 and 2 produced on borrowed funds
will be reduced. Hence, there will be 4 decision variables for this problem. Assume
that all units of each model are sold as they are produced to independent distributors
and that the average rate of turnover of accounts receivable is three months. The
funds borrowed to produce one unit of model 1 or 2 will be repaid approximately three
months later; that is, (Php50 x 12X¹) and (Php100 x 12X¹). (a) Give the decision
variables (Hint: 4 decision variables) (b) Formulate the complete linear programming
model.
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