The total cost of the order is T=6b+2wT=6b+2w, to find the constraints we have to follow the following procedure
Procedure:
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+2wT=6b+2w
Her budget is $85. So, total cost is less than or equal to 85.
6b+2w\leq 856b+2w≤85 ...(i)
For maximum number of bath towels, the number of wash cloths is 0.
6b+2(0)\leq 856b+2(0)≤85
6b\leq 856b≤85
Divide both sides by 6.
b\leq \dfrac{85}{6}b≤6 85
b\leq 14.167b≤14.167
For maximum number of wash cloths, the number of bath towels is 0.
6(0)+2w\leq 856(0)+2w≤85
2w\leq 852w≤85
Divide both sides by 2.
w\leq \dfrac{85}{2}w≤ 2 85
w\leq 42.5w≤42.5
Therefore, the required constraints for maximum of washcloths or bath towels are w\leq 42.5w≤42.5 and b\leq 14.167b≤14.167 respectively.
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