X Bus Econ 7.5.10 sells for $9.40. Acompany makes three types of candy and packa

Question

X Bus Econ 7.5.10 sells for $9.40. Acompany makes three types of candy and packages them in three assortments. Assortment sour, 4 lemon, and 12 lime candies, and sells f $11.00. I contains 4 ll contains 12 sour,4 emon, and 4 me candies, and sells for $7.60. ortment lll contains 8 sour, 8 lemon, and 8 ime candies, and candies costs per piece of candy are $0.20 for sour, $025 for lemon, and so 30 for ime. They can make 5.000 sour, lemon, and 5.800 weekly How many boxes of each type should the company produce each week in order to maximize its p What is the maximum profit? The maximum profitis s when boxes of assortment I, boxes of assortment and boxes of assortment ll are produced

Explanation / Answer

x - assortment 1

y -assortment 2

z -assortment 3

profit in   assortment 1 = (9.40 -0.2*4-0.25*4-0.3*12)= 4

profit in   assortment 2 = (7.60 -0.2*12-0.25*4-0.3*4)= 3

profit in   assortment 3 = (11-0.2*8-0.25*8-0.3*8)= 5

maximize 4x+3y+5z

x>0 , y> 0,z>0

4x + 12 y + 8 z < 5000

4x+4y+8z < 4200

12x+4y+8z < 5800

x = linprog(f,A,b) solves min f'*x such that A*x b.

A = [4 12 8 ; 4 4 8 ; 12 4 8 ; -1 0 0 ;0 -1 0 ; 0 0 -1];

b =[5000;4200;5800;0;0;0];
f =[-4 -3 -5] ;

x = linprog(f,A,b)

x =

200.0000
100.0000
375.0000

hence 200 assortment 1 , 100 assortment 2, 375 assortment 3 . are produced

profit

=200*4+3*100+5*375 = 2975

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