Textbook Problems Ch$.3-9,10,11$

Irwin Textile Mills produces two types of cotton cloth$-$denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires $7\mathrm{.}5$ pounds of raw cotton per yard, whereas denim requires $5$ pounds of raw cotton per yard. A yard of corduroy requires $3\mathrm{.}2$ hours of processing time; a yard of denim requires $3\mathrm{.}0$ hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is $510$ yards per month. The manufacturer has $6,500$ pounds of cotton and $3,000$ hours of processing time available each month. The manufacturer makes a profit of $$2\mathrm{.}25$ per yard of denim and $$3\mathrm{.}10$ per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit.

$8$

$9$

$10$

$11$

$12$

$13$

$14$

$15$

$16$

$17$

$18$

$19$

What would the profit be if the profit for corduroy increased from $3\mathrm{.}10$ to $4\mathrm{.}00?$

$($After you have completed this question change the data back to the original numbers given.$)$

$29$

Resources:

$\backslash$table$[[$Cotton $($lbs$),5\mathrm{.}0,7\mathrm{.}5,,,],[$Processing time $($hrs$),,,,,],[$Corduroy demand $($yds$),,,$Aeft over,,$]]$

$\backslash$table$[[$Products:$],[($Ibs$)],[$time $($hrs$)],[$mand $($yds$)]]$

$\backslash$table$[[$Denim$,$Corduroy$]]$

$\backslash$table$[[,,],[$Available$,$Usage,Left over$],[,,],[,,]]$

Hint:

The maximum demand for Corduroy is $510$ yards per month. There is not a similar Denim constraint: In the Corduroy constraint row, place $0$ in the Denim column, $1$ in the Corduroy column, and $510$ in the Available column. The Usage formula should follow the same pattern as the Cotton Usage formula and the Processing time Usage formula.