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ABCO manufactures two products X and Y . ABCO's manager is interested in production and liquidity planning for the next two weeks of operation. The
ABCO manufactures two products X and Y ABCO's manager is interested in production and liquidity
planning for the next two weeks of operation. The first week has four working days and the second week has
five working days. Each working day has one eighthour shift.
The firm has machines that can be used to produce both X and Y A unit of product X
takes hours of machine time, whereas a unit of Y takes hours. Sales of product Y cannot exceed
units during the next two weeks whereas there is no such restriction on the sales of product X Within those
limits ABCO does not produce on inventory and sells immediately what it produces. Sales price, wages to
labor, and cost of raw material per unit of product X and product Y do not vary over time and are given in
Table
Wages are proportional to production volume and paid in the week when production occurs, raw materials
are bought on credit of one week and delivered immediately, ie ABCO uses "justintime" delivery on a
weekly basis and maintains no inventory of raw materials for its current products. All sales are on credit,
and payments are received one week from the date of sale. The salary of the manager is $ per week; it
is not affected by the production volume, but it is paid weekly like the wages are. The balance sheet at the
beginning of the planning period is given in Table
From it we see that ABCO receives $ from accounts receivable and pays out $ at the start
of the first week. As a matter of policy, ABCO maintains inventories of $ in parts of some obsolete models. The current balance of marketable securities is earmarked for tax payments which are due later in the year: ABCO maintains a minimum cash balance of $ and has an open line of credit of $ from a local bank. This line of credit is presently fully used, but repayment and interest payments on its loans are scheduled for later in the year. In order to preserve a favorable picture of the firm's financial situation, the manager has agreed with the local bank that ABCO's "quick ratio" should not drop below
Verify that at the beginning of the period ABCO has a quick ratio greater than or equal to Show your calculations. The "quick ratio" is defined as
Quick Ratio Current Assets InventoriesCurrent Liabilities
Let
x: the number of units X produced and sold in week
y: the number of units Y produced and sold in week
x: the number of units X produced and sold in week
y: the number of units Y produced and sold in week
Formulate the problem of finding a profit optimal production mix for ABCO that is within the various
physical and policy restrictions as well as the limited scope of ABCO's financial capabilities as a
twoperiod linear program in the above four variables.
Compute a profit optimal product mix for ABCO using an LP solver. What is the optimal profit
ABCO can obtain?
To ensure a "smooth" production schedule ABCO's management wants that the two weekly production volume to schedule for product X and product Y respectively, do not fluctuate too widely. More precisely, management wants the absolute difference of the production volume of product X to not exceed of the total production volume for product X over the two periods and likewise for product Y Reformulate the linear program to include these considerations. What are the optimal production volume to be scheduled and what is the optimal profit for the changed linear program? How much does it cost ABCO to smooth its production this way? How does this answer change if management insists on a maximum fluctuation of rather than
Summarize your answers in a brief report, which also includes a listing of your GAMS model.
in dollars per unit Product X Product Y
Sales Price $ $
Labor $ $
Raw materials $ $
Profit $ $
Table: Cost and revenue data in dollars per unit
Assets Liabilities and Equity
Cash $ Accounts payable $
Marketable securities $ Bank loan $
Accounts receivable $ Current liabilities $
Inventories $ Longterm debt $
Current assets $ Net equity $
Fixed assets $
Total assets $ Total Liabilities & Equity $
Table: ABCO's Balance sheet as of the beginning of the planning period
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