Table $8-9$

As the high bidder on a monstrous storage locker in Rancho Cucamonga, Darrell discovers much to his dismay that no collectibles or priceless works of art have been seeded in his locker. Instead he finds cases and cases of raw leather, zippers, packets of dye, and spools of thread. After some thorough research on typical prices, Darrell concludes that his cost of the leather is $$2$ per yard, his zipper cost if $$1$ per foot, the dye is $$1$ per packet and the thread is fifty cents per foot.

They don't call him "The Gambler" for nothing, and he is determined to find a way to profit from this misfortune as well as shed the burden of his son Brandon, who isn't much of an asset in the storage wars. He sets Brandon up with a small production business and, using his connections, manages to land contracts to supply leather purses, pants, backpacks and jackets that can be dyed to match current market trends. $"$In fashion, one day you're in and the next day you're out," Darrell explains to Brandon as he reviewed the contracts he had arranged. $"$We can make enough to get you out of the house now that I have $60,000$ yards of leather, $50,000$ feet of zipper material, $100,000$ dye packets and $200,000$ feet of thread."

One local distributer has placed an order for at least $5,000$ purses and is willing to increase the order to a maximum of $10,000$ if sales are strong. A purse requires $0\mathrm{.}25$ yards of leather, a one foot length of zipper material, one dye packet and two feet of thread. Darrell charges $$41\mathrm{.}50$ for each one shipped. Another distributor is more interested in apparel and has placed orders for both pants at $$33\mathrm{.}50$ and jackets at $$104.$ They want at least $10,000$ jackets up to a ceiling of $15,000$ and at least $10,000$ pairs of leather pants. As you might imagine, there is no limit to the number of pairs of leather pants that can be sold. A leather jacket requires $1\mathrm{.}5$ yards of leather, three feet of zipper material, two dye packets and eight feet of thread. Leather pants take a full two yards of leather, six inches of zipper material, two dye packets and six feet of thread. Yet another distributor is keen on backpacks and sees a market for at least $2,500$ backpacks but is unwilling to take more than $7,500.$ Each backpack requires a half yard of leather, two feet of zipper material, one dye packet, and three feet of thread, and Darrell ships them to this distributor at $$22\mathrm{.}50.$

Use the information in Table $8-9$ to formulate a constraint for the use of leather.

$0\mathrm{.}25L+1Z+1D+2T60,000$

$0\mathrm{.}25Pu+2Pa+0\mathrm{.}50B+1\mathrm{.}5J60,000$

$0\mathrm{.}25L+1Z+1D+2T60,000$

$0\mathrm{.}25Pu+2Pa+0\mathrm{.}50B+1\mathrm{.}5J60,000$