Question 1110667
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Let x be the number of pounds of the first mixture and y be the number of pounds of the second.  Then
(1) {{{.6x+.2y <= 7600}}}  he has 7600 pounds of peanuts
(2) {{{.3x+.5y <= 5800}}}  ... and 5800 pounds of almonds
(3) {{{.1x+.3y <= 3000}}}  ... and 3000 pounds of cashews<br>
He wants to maximize his revenue, given that the first mixture sells at $8.44 per pound and the second sells at $3.17 per pound.  So the objective function to be maximized is
{{{8.44x + 3.17y}}}<br>
In slope-intercept form, the three constraint equations are
(1) {{{y = -3x+38000}}}
(2) {{{y = (-3/5)x+11600}}}
(3) {{{y = (-1/3)x+10000}}}<br>
Algebra or a graphing calculator show that the vertices of the feasibility region are
(0,0)
(38000/3,0)
(11000,5000)
(6000,8000)
(0,10000)<br>
Evaluating the objective function at each of those vertices shows the maximum revenue is $108,690 at (11000,5000).