Question

Kimberly is ordering bath towels and washcloths for the inn where she works. The total cost of the order is T=6b+2w, where T is the total cost, b is the number of bath towels, and w is the number of washcloths.. Her budget is $85. Describe the constraints.
She can order a maximum of washcloths or bath towels.

Answer 1

Given:

The total cost of the order is

$T=6b+2w$

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,

$T=6b+2w$

Her budget is $85. So, total cost is less than or equal to 85.

$6b+2w\leq 85$       ...(i)

For maximum number of bath towels, the number of wash cloths is 0.

$6b+2(0)\leq 85$

$6b\leq 85$

Divide both sides by 6.

$b\leq \dfrac{85}{6}$

$b\leq 14.167$

For maximum number of wash cloths, the number of bath towels is 0.

$6(0)+2w\leq 85$

$2w\leq 85$

Divide both sides by 2.

$w\leq \dfrac{85}{2}$

$w\leq 42.5$

Therefore, the required constraints for maximum of washcloths or bath towels are $w\leq 42.5$ and $b\leq 14.167$ respectively.