"the munchies cereal company makes a cereal from several ingredients. two of the ingredients, oats and rice, provide vitamins a and b. the company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 milligrams of vitamin a and 12 milligrams of vitamin b while minimizing cost. an ounce of oats contributes 8 milligrams of vitamin a and 1 milligram of vitamin b, whereas an ounce of rice contributes 6 milligrams of a and 2 milligrams of b. an ounce of oats costs $0.05, and an ounce of rice costs $0.03. a. formulate a linear programming model for this problem. b. solve this model by using graphical analysis."

8x + 6y >/= 48 ......1

x + 2y >/= 12 .......2

The cost function is given as;

C = 0.05x + 0.03y .........3

The minimum cost is $0.24 at (0,8)

That is 0 ounces of oats and 8 ounces of rice.

Step-by-step explanation:

let x represent the number of ounces of oats

And y represent the number of ounces of rice

For Vitamin A

Minimum requirements = 48mg

x ounces of oats contribute 8mg × x

y ounces of Rice contribute 6mg × y

Therefore, we have;

8x + 6y >/= 48 ......1

For Vitamin B

Minimum requirements = 12mg

x ounces of oats contribute 1mg × x

y ounces of Rice contribute 2mg × y

Therefore, we have;

x + 2y >/= 12 .......2

The cost function is given as;

C = 0.05x + 0.03y .........3

Attached is the graphical representation.

The feasible points are (x,y) = (0,8),(2.4,4.8),(12,0)

The minimum cost is determined by substituting each point into the cost function

For (0,8)

C= 0.05(0) + 0.03(8)

C = $0.24

For (12,0)

C= 0.60

For (2.4,4.8)

C= $0.264

The minimum cost is $0.24 at (0,8)

.

step-by-step explanation:

.

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).