operation research question

Problem 3 (20 points) As the manager for a line of trendy clothing, you are meeting with your production manager to determine next month's production plan. You need to determine the quantity of each clothing item to produce, ensuring that you don't exceed your plant's limited capacity, sparse resources and anticipated demand. You have already determined the price for each of your items. The requirements are below: Item Material Selling Price Labor and Machine Requirements Cost Checkered Pants 3 yards of wool $300 $160 2 yards of acetate Polka dot sweater 1.5 yards of polyester $450 $150 Silk shirt 1.5 yards of Silk $180 $100 Silk tie 0.5 yard of Silk $120 $60 Button down shirt 2 yards of rayon $270 $120 1.5 yards of acetate Blazer 2.5 yards of wool $320 $140 1.5 yards of acetate Velvet jacket 3 yards of velvet $350 $175 2 yards of acetate Striped sweater 1.5 yards of cotton $1330 $60 Cotton socks (pair) 0.5 yard of cotton $75 $40 Velvet shirt 1.5 yards of velvet $200 $160 Polo shirt 1.5 yards of rayon $120 $90 You have ordered: 45,000 yards of wool, 28.000 yards of acetate, 9.000 yards of polyester. 18.000 yards of silk, 30,000 yards of cotton, 20,000 yards of velvet and 30,000 yards of rayon. Their prices per yard are: Material Price per yard Wool $9 Acetate $1.50 Polyester $60 Silk $13 Rayon $2.25 Velvet $12 Cotton $250 Any material you do not use can be sent back to the manufacturer for a full refund, but scraps cannot. To produce the silk shirt or the striped sweater, 2 yards of silk or cotton are needed, respectively. Of these 2 yards, 1.5 is used for the garment and 0.5 yards are left as scrap. This half a yard is used for the silk fie (from the silk shirt scrap) and a pair of cotton socks (from the striped sweater scrap). Therefore when a silk shirt is produced a silk tie is also produced Likewise, whenever a striped sweater is produced, a pair of cotton socks is produced. It is possible though to produce a siliktie or cotton sock pair without producing a silk shirt or striped sweater, respectively