Question

А percent, WHIC CX Can ve any murupicur VU TUMU 70 W JU70. 39. A textile company produces shirts and pants. Each shirt requires three square yards of cloth, and each pair of pants requires two square yards of cloth. During the next two months the following demands for shirts and pants must be met (on time): month 1, 2000 shirts and 1500 pairs of pants; month 2, 1200 shirts and 1400 pairs of pants. During each month the following resources are available: month 1, 9000 square yards of cloth; month 2, 6000 square yards of cloth. In addition, cloth that is available during month 1 and is not used can be used during month 2. During each month it costs $10 to produce an article of clothing with regular-time labor and $16 with overtime labor. During each month a total of at most 2400 articles of clothing can be produced with regular- time labor, and an unlimited number of articles of clothing can be produced with overtime labor. At the end of each month, a holding cost of $1 per article of clothing is incurred. (There is no holding cost for cloth.) a. Determine how to meet demands for the next two months (on time) at minimum cost. Assume that 100 shirts and 200 pairs of pants are already in inventory at the beginning of month 1.

Answer 1

Statement Showing the Total and Per Unit Cost Of Each Product                          

Particulars Units   Amounts($)
Month 1   
Production Cost
Shirt 1900  
Pant   1300  
Total Production 3200  
Less Production Without Overtime @$10    2400 24000

Production with overtime @$16 P.u 800 12800

Storage Cost @ $1 P.u on 3200 units   3200 3200
Total   3200 40000

Per unit Cost ( $40000/3200 units) = $12.50
Month 2                         
Production Cost During the month                          
Shirt 1200  
Pant 1400  
Total Production   2600  
Less: Production Without Overtime @ $10                 2400 24000
Production with Overtime @ $16    200   3200
Storage Cost @ $1 for 2600 units 2600

Total Cost 29800
Per Unit Cost($29800/2600 units) $11.46

Working Note              
1) Production of closths for Two months              
Particulars Shirts   Pant
Month 1              
Demand 2000   1500
Less: Opening Stock    100 200
Production during Month 1 1900   1300
Month 2              
Demand 1200   1400
Less: Opening Stock Nil Nil
Production During Month 2 1200   1400

2) There is no information regarding the material and labour cost per unit separately. Only a total cost is given. Also there is no differnce of cost is given for Shirt and pant. An uniform rate of cost @ $10 is given. So, the information regarding stock of cloths and labour hours is immaterial.