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A company produces and sells four grades of industrial solvents -
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A company produces and sells four grades of industrial solvents - A, B, C, and D. The selling price per gallon of each grade of solventis $6.40, $5.00, $4.20, and $3.50 respectively.  Because of demand limitations, the company can sell at most 100,000 gallons of solvent A; 300,000 gallons of solvent B; 360,000 gallons of solvent C; and 220,000gallons of solvent D. 

The solvents are produced by blending two types of liquid ingredients: Ingredient1 and Ingredient2. The cost price per gallon for the ingredients are $3.20 for Ingredient1 and $2.40 for Ingredient2. At most 400,000 gallons of Ingredient1 and 600,000 gallons of Ingredient2 are available.

Regulations require a minimum percentage by volume of Ingredient1 in each grade of solvent: 60% for A, 50% for B, 40% for C, and 10% for D.

For your convenience, the information presented above is summarized in the tables below:

Solvent grade

A

B

C

D

Selling price per gallon

 $   6.40

 $  5.00

 $  4.20

 $  3.50

Maximum quantity allowed (gallons)

100,000

300,000

360,000

220,000

Minimum % of Ingredient1 required

60%

50%

40%

10%

Availability (gallons)

Price per gallon

Ingredient1

400,000

 $   3.20

Ingredient2

600,000

 $  2.40

The company must determine an optimal production plan so as to maximize their profits subject to the applicable constraints. 


Formulate the problem as a linear program (4 points)

Define the decision variables:

Specify the objective function:

Specify the constraints:


Solve the linear program and report your optimal solutions (4 points)

What is the maximum profit attainable under an optimal plan? (2 points)

Maximum Profit = 

$

How many gallons of each ingredient should be used to produce each grade of solvent under this optimal plan? (1 point)

Quantity (in gallons)

A

B

C

D

Ingredient1

Ingredient2

How many gallons of each ingredientis used up under this optimal plan? (1 point)

Quantity (in gallons)

Used

Available

Ingredient1

400,000

Ingredient2

600,000

At most how much should the company be willing to pay per gallon for additional quantities of the ingredients? Justify your answer. (4 points)

The maximum amount that the company should be willing to pay for each additional gallon:

Ingredient1:

$

per gallon.

Ingredient2:

$

per gallon.

Reasoning:


The Marshall family is very conservative financially. They have a retirement plan where John works and share a joint checking account at their bank. They keep a lot of money in their checking account to cover short-term needs and emergencies. Both of them want to step up to a higher interest rate than a checking or savings account pays, and at the same time stay with their bank.1) What would be your suggestion for the next account John and Shelia should open?A) Series EE bondsB) Certificates of depositC) Money market deposit accountD) Money market mutual fundsE) A, B, or C above2) Which of the following is not an advantage of a CD as a cash management alternative?A) High interest rateB) Fixed rate of interestC) It is insured.D) Pays money market interest ratesE) Lends itself well to automated payroll deduction plan3) Money market deposit accounts offer some advantages. Select the one or ones below.A) They are insured.B) They may have limited checking privileges.C) They have relatively attractive rates of return.D) They have variable market interest rates.E) all of the above4) What financial principle do they need to understand better?A) Time Value of Money.B) Taxes effect personal finance decisions.C) Stuff happens: The importance of liquidity.D) Risk and return go hand in hand.E) All of the above are important to their situation.5) The Marshalls have been thinking about the financial principle - Pay Yourself First. Being very conservative, they might consider having their bankA) Sell them a risky mutual fund.B) Send them a monthly reminder to make a deposit in their savings.C) Do a direct deposit of John's paycheck into their checking account.D) Do a direct deposit of some of John's paycheck into a savings fund.E) Both C and D above6) You have $7,500 in a 12 month Certificate of Deposit that pays 8% APR that compounds quarterly. What is the APY or effective rate on your investment?A) 8.0%B) 8.24%C) 8.36%D) Not enough information available7) The FDIC does not insure deposits with Online Commercial Banks.Answer: True/FALSE8) In choosing among cash management alternatives, one shouldA) Consider the safety and risk involved.B) Examine the service and convenience available.


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