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I have a question about one of the constraints in an LP from my homework.

A company produces two products, A and B. The sales volume for A is at least 80% of the total sales of both A and B. However, the company cannot sell more than 100 units of A per day. Both products use one raw material, of which the maximum daily availability is 240 lb. The usage rates of the raw material are 2 lb per unit of A and 4 lb. per unit of B. The profit units for A and B are \$20 and \$50, respectively. Determine the optimal product mix for the company.

If we let $A=$ units of product A and $B=$units of product B, then we'll $$\text{maximize }z=20A+50B$$ subject to

\begin{align*} 2A+4B&\leq240 &&\text{(raw material availability)}\\ A&\leq100 &&\text{(sales limit of A)}\\ -0.2A+0.8B&\leq0 &&\text{(sales of A at least 80%)}\\ A,B&\geq0 &&\text{(sign restrictions)} \end{align*}

I was able to get everything, except I don't quiet understand how my professor found the constraint $-0.2A+0.8B\leq0$. Could somebody please provide a more detailed explanation? Thank you.

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"The sales volume for A is at least 80% of the total sales of both A and B": $$ A\geq 0,8 (A+B) $$ Subtract $A$ on both sides and you get $$ 0\geq -0.2A+0.8B $$

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  • $\begingroup$ Nailed it! Thanks, @Reinhard! $\endgroup$ – jbrow35 Feb 8 '17 at 21:50

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