On Best Corrected Mixture Problems in Metallurgy: A Case Study

<table class="table-group" id="tab10"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left"> <svg height="9.16851pt" id="M237" style="vertical-align:-0.2455301pt" version="1.1" viewbox="-0.0498162 -8.92298 9.79486 9.16851" width="9.79486pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M397 143C384 252 309 299 234 299C151 299 67 242 67 142C67 29 167 -15 264 -15C419 -15 547 68 547 204C547 336 385 381 385 491C385 582 483 644 560 644C613 644 668 624 668 563C668 499 620 463 559 456V435C627 435 701 491 701 564C701 648 628 680 561 680C454 680 308 615 308 472C308 340 465 297 465 191C465 75 365 15 272 15C192 15 129 67 129 137C129 212 192 256 241 256C296 256 345 244 377 139L397 143Z" id="g198-20"></path><glyph.data ascent="687" descent="-226" horiz-adv-x="743" vert-adv-y="743"></glyph.data></g></svg></td><td class="align_left"><span style="width: 14.9879ptpx;"><svg height="10.2019pt" id="M238" style="vertical-align:-0.2455091pt" version="1.1" viewbox="-0.0498162 -9.95639 14.9879 10.2019" width="14.9879pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M397 143C384 252 309 299 234 299C151 299 67 242 67 142C67 29 167 -15 264 -15C419 -15 547 68 547 204C547 336 385 381 385 491C385 582 483 644 560 644C613 644 668 624 668 563C668 499 620 463 559 456V435C627 435 701 491 701 564C701 648 628 680 561 680C454 680 308 615 308 472C308 340 465 297 465 191C465 75 365 15 272 15C192 15 129 67 129 137C129 212 192 256 241 256C296 256 345 244 377 139L397 143Z" id="g198-20"></path><glyph.data ascent="687" descent="-226" horiz-adv-x="743" vert-adv-y="743"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.659,-5.741)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z" id="g50-98"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="514" vert-adv-y="514"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Empty</td><td class="align_left">Empty</td></tr><tr><td class="align_left">empty</td><td class="align_left">Nonempty, closed and bounded (compact)</td></tr><tr><td class="align_left">Nonempty, closed and bounded (compact)</td><td class="align_left">empty</td></tr><tr><td class="align_left">Nonempty, closed and bounded (compact)</td><td class="align_left">Nonempty, closed and unbounded</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Relationship between the feasible sets <svg height="9.16851pt" id="M235" style="vertical-align:-0.2455301pt" version="1.1" viewbox="-0.0498162 -8.92298 9.79486 9.16851" width="9.79486pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M397 143C384 252 309 299 234 299C151 299 67 242 67 142C67 29 167 -15 264 -15C419 -15 547 68 547 204C547 336 385 381 385 491C385 582 483 644 560 644C613 644 668 624 668 563C668 499 620 463 559 456V435C627 435 701 491 701 564C701 648 628 680 561 680C454 680 308 615 308 472C308 340 465 297 465 191C465 75 365 15 272 15C192 15 129 67 129 137C129 212 192 256 241 256C296 256 345 244 377 139L397 143Z" id="g198-20"></path><glyph.data ascent="687" descent="-226" horiz-adv-x="743" vert-adv-y="743"></glyph.data></g></svg> and <svg height="10.2019pt" id="M236" style="vertical-align:-0.2455091pt" version="1.1" viewbox="-0.0498162 -9.95639 14.9879 10.2019" width="14.9879pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M397 143C384 252 309 299 234 299C151 299 67 242 67 142C67 29 167 -15 264 -15C419 -15 547 68 547 204C547 336 385 381 385 491C385 582 483 644 560 644C613 644 668 624 668 563C668 499 620 463 559 456V435C627 435 701 491 701 564C701 648 628 680 561 680C454 680 308 615 308 472C308 340 465 297 465 191C465 75 365 15 272 15C192 15 129 67 129 137C129 212 192 256 241 256C296 256 345 244 377 139L397 143Z" id="g198-20"></path><glyph.data ascent="687" descent="-226" horiz-adv-x="743" vert-adv-y="743"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,9.659,-5.741)"><path d="M490 97L476 124C442 96 405 70 398 70C392 70 390 78 396 114C419 243 448 379 463 432L457 436C446 436 431 439 418 442C393 447 368 451 343 451C281 451 204 418 155 381C74 320 24 206 24 107C24 23 59 -12 88 -12C118 -12 155 5 191 34C236 70 290 122 328 177H330L312 84C296 0 311 -12 331 -12C355 -12 425 24 490 97ZM374 387C371 367 360 299 347 264C323 202 187 53 142 53C128 53 113 73 113 120C113 224 157 332 221 380C241 395 274 403 303 403C330 403 360 395 374 387Z" id="g50-98"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="514" vert-adv-y="514"></glyph.data></g></svg>.

Mathematical Problems in Engineering

On Best Corrected Mixture Problems in Metallurgy: A Case Study

Table 10