Question

A dairy company gets milk from two dairies and then blends the milk to get the desired l costs S0.80 per gallon. Al most $144 is available for purchasing milk. Dairy I can supply at most 50 80 gallons averaging 29% butterfat Answer parts a-d of butterfat Milk from dairy 1 costs $2.40 per gallon, and milk rod with All supporting written work showing how you derived your final answers for this portion of the problem should be shown on your paper in your grade. You are not allowed to enter your answer for the problem into MML Round your final answers to the nearest whole number. Your final answers must also include the unit(s) of measure.) including your final answers b. What is the written work showing how you derived your final answer for this portion of the problem should be shown on your paper, in your grade. You are not allowed to enter your answer for the problem into MML All s Failure to do will cause a point(s) Round your final answer to two decimal places, Your final answer must also include the unit(s) of measure ) c. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce. written work showing how you derived your final answers for this portion of the problem should be shown on your paper, including your final answers All s Failure to do will cause a point(s) reduction in your grade. You are not allowed to enter your answer for the problem into MML Round your final answers to the nearest whole number. Your final answers must also include the unit(s) of measure) d. Is there any way all this capacity could be used while still meeting the other constraints? Read each of the statements below Determine which one is correct, write the entire correct statement on your paper - failute to do so will result in full credit not being given for your written answer You ill not be allowed to select/type your answer into MM A No. Any more milk purchased from either dairy will go over budget B Yes, 10 more gallons can be bought from dairy I without going over budget

Answer 1

1. (a). Let, number of gallons of milk purchased from dairy 1 = x

Number of gallons of milk purchased from dairy 2 = y

Objective function :- Maximize butterfat

Max z = 0.039x + 0.029y

Constraints:-

2.40x + 0.80y <= 144 ... equation (1)

x <= 50 ..equation (2)

y <= 80 ...equation (3)

x + y <= 100 ... equation (4)

On solving these inequalities we get

x = milk from dairy 1 = 40 gallons

y = milk from dairy 2 = 60 gallons

(b). Butterfat = ( 0.039 × 40 ) + ( 0.029 × 60 ) = 3.30 gallons

(c). Additional milk dairy 1 could produce = 50 - 40 = 10 gallons

Additional milk dairy 2 could produce = 80 - 60 = 20 gallons

(d).Amount spend to purchase milk = ( 2.40 × 40 ) + ( 0.80 × 60 ) = $144

Thus, We can not purchase any more milk from from either dairy because it will go over budget.

Option (A) is the correct answer.