Mike may has been told that each day he needs at least 16 units of vitamin a, at least 5 units of vitamin b-1, and at least 20 units of vitamin c. each brand x pill contain 8 units of vitamin a, 1 of vitamin b-1, and 2 of vitamin c, while each brand z pill contains 2 units of vitamin a, 1 of vitamin b-1, and 7 of vitamin c. a brand x pill costs 15 cents, and a brand z pill costs 30 cents. how many pills of each brand should he buy to minimize his daily cost? what is the minimum cost?

cost = 15*3 + 30*2 =105 cents

where X pills =3 and Z pills =2  

Explanation:

Let x be the number of units of pill X and z be number of units of pill Z

so the objetive is to minimize cost

Minimize 15x + 30z

we know that

8x + 2z >=16 -i) vitamin A constraint

x + z >=5 -ii) vitamin B1 constraint

2x + 7z >=20 -iii) vitamin C constraint

we know that x>=0 and z>=0

On solving through MS-EXCEL (Image Attached)

cell I8 represents x and J8 represents z we get x=3 , z=2

cells to be varied I8:J8

8x + 2z >=16 represented by K5=SUMPRODUCT(I5:J5,I8:J8) where K5>=16

x + z >=5 represented by K6 =  SUMPRODUCT(I6:J6,I8:J8) where K6>=5

2x + 7z >=20  represented by K7 = =SUMPRODUCT(I7:J7,I8:J8) where K7>=20

cell to be minimized

NB = SUMPRODUCT(I8:J8,N5:O5) Minimize 15x1 + 30x1

cost = 15*3 + 30*2 =105 cents

where X pills =3 and Z pills =2  

answer; offer in store wine and beer samples;