Use the Data Shown Below to Answer the Following Question(s)

question 14

Multiple Choice

Use the data shown below to answer the following question(s) .
Hudson's Creators is a company that produces embroidered clothes.Forecasts of sales for the next year are 200 in the autumn,450 in the winter,and 100 in the spring.Plain clothes are purchased from a supplier for $25.The cost of capital is estimated to be 28% per year (or 7% per quarter) ; thus,the holding cost per item is 0.07($25) = $1.75 per quarter.Hudson hires art students part-time to produce his designs during the autumn,and they earn $6.50 per hour.Because of the high demand for part-time help during the winter holiday season,labor rates are higher in the winter,and workers earn $8.00 per hour.In the spring,labor is more difficult to keep,and the owner must pay $7.25 per hour to retain qualified help.Each embroidered cloth takes 2 hours to complete.Define the model based on how the production should be planned over the three quarters to minimize the combined production and inventory holding costs.
Use the following terms to define the decision variables:
P_A = amount to produce in autumn
P_W = amount to produce in winter
P_S = amount to produce in spring
I_A = inventory held at the end of autumn
I_W = inventory held at the end of winter
I_S = inventory held at the end of spring
Suppose that Hudson must rent some equipment to produce his products,which costs $75 for three months.The equipment can be rented or returned each quarter,so if nothing is produced in a quarter,it makes no sense to incur the rental cost.
The fixed costs can be incorporated into the model by defining an additional set of variables:
Y_A = 1 if production occurs during the autumn,and 0 if not
Y_W = 1 if production occurs during the winter,and 0 if not
Y_S = 1 if production occurs during the spring,and 0 if not
-Which of the following is the basic material balance equation for the winter season?

• A)P_W + I_W = 100
• B)P_W - I_W ≥ 450
• C)P_W + I_A - I_W ≤ 100
• D)P_W + I_A - I_W = 450

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