Question

Suppose you want to design a salad having two main items, lettuce and tomato. Suppose

that each gram of lettuce provides 2 units of vitamins and 2 units of minerals and each gram
of tomato provides 1 unit of vitamins and 2 units of minerals. The cost of lettuce is 100

Rs/gram and the cost of tomato is 20 Rs/gram.The salad must provide at least 8 units of vitamins and 10 units of minerals.

How many grams of each item should be provided in order to meet the requirements of

vitamins and minerals for the least cost? What will this salad cost? Use the graphical

method.

Present both primal and dual forms, including their graphs.​

Answer 1

Answer:

Rs 160

Step-by-step explanation:

design a salad having two main items, lettuce and tomato. Suppose

each gram of lettuce provides 2 units of vitamins and 2 units of minerals

L = 2 V  + 2M

each gram  of tomato provides 1 unit of vitamins and 2 units of minerals.

T = V + 2M

Cost of Lettuce = 100L    

Cost Of Tomato = 20T

V ≥ 8

M ≥ 10

Let say  L gram of Lettuce & T grams of tomato is used

LL = 2L V  + 2L  M

TT = T V  + 2T M

2L + T  ≥ 8

2L + 2T  ≥ 10

100L + 20 T

Lettuce Tomato 100L + 20T    Vitamin    Minearls

0          8          160                 8               16

1          6           220                8               14

2           4           280                 8               12

3           2           340                  8               10

4            1           420                  9              10

5            0           500                 10              10

Best option is to use 8 gm of tomato only

Cost of Salad = Rs 160