Question

Midtown Manufacturing Company makes plastic plates and cups, both of which require time on two machines. Producing a unit of plates requires 1 hour on Machine A and 2 hours on Machine B, while producing a unit of cups requires 3 hours on Machine A and 1 hour on Machine B. Each machine is operating for mostly 15 hours per day. Each unit of plates brings in $10 in profit for the company and each unit of cups brings in $12 in profit. a.) Write a system of inequalities expressing these conditions and graph the feasible region. b.) Find the profit maximizing combination of plates and cups this company can and should produce.

Answer 1

Solution! ons (a):- Here, we assuming the number of plates and cups should be produced be x, and X₂ Profit 10X, +1282 for machine (A) x +3725 15 0 for machine (B) and X, X27,0 2x + x2 < 15 3 corner points :- (0,0) (0,5) (75,0 using et and , (multiplying en hy 2) X;+372=15 → 251,+ 6X2-30 ax + x2 = 15 2x + x2 =15 5x2 = 15 12 = 3 x = 15-342 = 15-343 n 15 (2 ) =) (6,3) — 5 feasible Region K(63) (1) 0 7.5 >x, 15 Cs Scanned with CamScanner

Ans (6) finding profits! - (0) now, we have four corners de points. (0,0), (0,5) (7-5,0), (6,3) and profit = 10X1+1222 = 6 = 10yo +12*5 = 60 a(0,0) *(0,5) ^ (7.570) A(613) - 1097-5+1240 ? =75 = 10x6 + 12x3 = 96 Thus, the maximum of profit is 96, which comes On combination of (2, H2) = 16,3) Therefore, the company should produce the combineña of Plates and lips are 6 and 3 respectively cs Scanned with CamScanner