Algebra 2 help Solving Linear Programming Problems?

James Langmyer: Let x be the number of old members and y be the number of new members.The city Recreation Department agrees to pay each old member $10 and each new member $8 for their services.[Amount Earned] = 10x + 8yThe club has at most 9 old members and at most 8 new members.x y The Department will hire at least 6 students, but no more than 15.x + y >= 6x + y There must be at least 3 new members and at least 4 old members.x >= 4y >= 3The number of new members must be at least 1/2 the number of old members, but less than 3 times the number of old members.y >= 1/2xy Are all of the constraint equations in standard form [(a_1)x + (a_2)y x y x + y >= 6 NO.x + y x >= 4 NO.y >= 3 NO.y >= 1/2x NO.y Let's convert [x + y >= 6] to standard form by multiplying both sides by -1:-1x + -1y Let's convert [x >= 4]:-1x + 0y [y >= 3]: 0x + -1y [y >= 1/2x]:(1/2)x + -1y [y Note that this equation is the same as y -3x + 1y Combining everything, we getmaximize 10x + 8ysubject to 1x + 0y 0x ! + 1y -1x + -1y 1x + 1y -1x + 0y 0x + -1y (1/2)x + -1y -3x + 1y Solving this program givesx = 9y = 610x + 8y = 138...Show more