Doug Turner Food Processors wishes to introduce a new brand of dog biscuits composed of chicken$-$ and liver$-$flavored biscuits that meet certain nutritional requirements. The liver$-$flavored biscuits contain $1$ unit of nutrient A and $2$ units of nutrient B; the chicken$-$flavored biscuits contain $1$ unit of nutrient A and $4$ units of nutrient B$.$ According to federal requirements, there must be at least $40$ units of nutrient A and $60$ units of nutrient B in a package of the new mix. In addition, the company has decided that there can be no more than $15$ liver$-$flavored biscuits in a package. If it costs $1$ to make $1$ liver$-$flavored biscuit and $2$ to make $1$ chicken$-$flavored, what is the optimal product mix for a package of the biscuits to minimize the firm$$s cost$?$ Formulate this as a linear programming problem.

What is the product ingredient mix? liver flavor biscuits $=$

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$,$ chicken flavor biscuits $=$

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What is the total cost of a package of dog biscuits using the optimal mix?

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cents

Are there any unused resources?

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If so$,$ in what constraint, and by how much?

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What if federal requirements for nutrient A was reduced by $5$ units, what would the overall cost be$?$