Given:
The total cost of the order is
[tex]T=6b+2w[/tex]
where, T is the total cost, b is the number of bath towels, and w is the number of wash cloths.
Her budget is $85.
To find:
The constraints, so that she can order a maximum of washcloths or bath towels.
Solution:
We have,
[tex]T=6b+2w[/tex]
Her budget is $85. So, total cost is less than or equal to 85.
[tex]6b+2w\leq 85[/tex] ...(i)
For maximum number of bath towels, the number of wash cloths is 0.
[tex]6b+2(0)\leq 85[/tex]
[tex]6b\leq 85[/tex]
Divide both sides by 6.
[tex]b\leq \dfrac{85}{6}[/tex]
[tex]b\leq 14.167[/tex]
For maximum number of wash cloths, the number of bath towels is 0.
[tex]6(0)+2w\leq 85[/tex]
[tex]2w\leq 85[/tex]
Divide both sides by 2.
[tex]w\leq \dfrac{85}{2}[/tex]
[tex]w\leq 42.5[/tex]
Therefore, the required constraints for maximum of washcloths or bath towels are [tex]w\leq 42.5[/tex] and [tex]b\leq 14.167[/tex] respectively.
