The Diet Problem 3.1.1 Eating for cheap on a very limited menu

A sandwich shop has a menu consisting of four items Turkey breast on a bun a club sandwich a veggie sub a breakfast sandwich nutritional data for each is summarized on table 3.1

sandwich type

	Turkey breast	club	veggie sub	breakfast sandwich
calories	280	320	230	470
fat grams	4.5	6	3	19
cholesterol	20	35	0	200
carbohydrates	46	47	44	53
fiber	5	5	5	5
protein	18	24	9	28
Vitamin A	8	8	8	10
vitamin C	35	35	35	15
calcium	6	8	6	25
iron	25	30	25	25

Daily nutritional guideline requirements for each category nutrition in table 3.1 are presented in table 3.2 table 3.2 daily nutritional guidelines

	Daily minimum	Daily maximum
calories	2000	300
fat grams	0	65
cholesterol	0	300
carbohydrates	50	300
fiber	25	50
protein	50	200
Vitamin A	40	200
vitamin C	40	200
calcium	40	200
iron	40	200

Suppose that sandwiches cost $6 Turkey breast, $5 club sandwich $3.50 veggie sub, and $5 breakfast sandwich. We seek to minimize the total daily cost of maintaining a diet that has compromised solely of these 4 sandwiches and fulfills the previously stated nutritional guidelines we will permit partial consumption of any sandwich and assume that the purchase price of any sandwich is prorated based on the fraction consumed for example consumption of 1/2 a sandwich will contribute to only $2.50 total cost.

A. how much do we expect to spend daily on consuming a combination of the 4 sandwiches that is least expensive.

B. determine that combination of sandwiches to be consumed daily

C. what is the total amount of each nutrition consume daily from the combination of sandwiches