Question

​Formulate the linear programming model for the issue​ algebraically by stating the:

1) Definition of Decision Variables,
2) Objective Function Equation,
3) Constraints Equations.

​​Set up and solve the problem using Excel.

Provide your answers and recommendations to the Manager of the company

General organization and formatting.

1. Richelieu Specialty Paints

Richelieu Specialty Paints is a company run by Amanda Richelieu. She is an artist and earned a BA degree with a major in Art and Design. The company was founded by Amanda’s father and he recently asked her to take over managing it so that he could retire. Amanda agreed and left her interior design job with an architecture firm to assume the role. She is keen to develop the business further.

The company makes a wide variety of paints, mostly targeted at fine artists. However, since Amanda has had experience in interior design she has determined that the company could apply its skills to develop new products for that industry and others.

She knows that she hasn’t yet developed her quantitative analysis skills to the point they need to be to run a company, so she is seeking assistance with four decisions that she needs to make. She would like to have a report from you providing recommendations for each decision, along with the background calculations that support your decisions.

Decision 1: Marketing - Advertising Placement

Amanda has a yearly advertising and promotions budget of $50,000. Her goal is to maximize the reach (the number of customers that see her company’s ads or other marketing efforts).

She is considering a mix of placing ads on art websites and in printed art magazines, as well as using targeted social media ad placements and appearances at art tradeshows. She wants to make sure that the company has an online presence, so would like to see at least 100 ads placed in any combination of websites and social media per year. However, she has data that suggests that if she advertises on the websites more than 60 times per year she will be wasting money. There are seven art tradeshows that the company could attend, but Amanda feels it is mandatory to attend at least the two most popular tradeshows. There are three major art magazines, each published monthly, that Amanda would like to advertise in. She could advertise in each of these once per month but would be comfortable reducing the frequency to a minimum of once every three months in each magazine and rotating the placements between the magazines.

The reach and cost of each type of ad placement or event is shown below:

	Art Websites	Social Media	Art Tradeshow s	Print Magazine Ads
Reach (number of people)	15000	12,000	5,000	10,000
Cost (dollars)	200	250	1,000	400

• ● Recommend the appropriate mix of advertising and promotions for the company.

• ● Also comment on what would change if Amanda doubled her advertising and promotions

  budget. Estimate the increased reach if the budget were to double.

Decision 2: Financial - Assets Investment

Richelieu Specialty Paints has been quite successful and has $1,500,000 cash to be invested. Amanda and her management team have developed four potential investments in addition to leaving the cash in a low interest deposit. The four new opportunities are:

1. Purchase some shares of a major supplier (25% risk of total loss, 13% expected return)
2. Invest in the research and development of a new product (50% risk of total loss, 60% expected

return)
3. Buy a selection of corporate bonds (10% risk of total loss, 6% expected return) 4. Buy a selection of government bonds (1% risk of total loss, 3% expected return)

Leaving the money in a low interest deposit is virtually riskless and has a 0.5% return.

Richelieu’s father had provided Amanda with some guidelines for investment, aimed at diversification and risk management. These are:

1. Invest a maximum of 40% of the total cash in any one of the four new opportunities to ensure some risk control.

2. Invest at least $100,000 in each of the four new opportunities to ensure some diversity.

3. Limit the total potential loss to $300,000, based on the risk factors indicated.

4. Ensure the highest return possible.

• ● Recommend how much money should be invested in each of the four new investments, as well as the low interest deposit.

• ● Also, comment on how this mix would change, and what would happen to potential return, if Amanda decided to take a more conservative approach and limit the total potential loss to $150,000.

  Decision 3: Operations - Materials Blending

  Richelieu Specialty Paints has begun making paints for the interior design market. The company starts the process by blending four base paint mixes together that they buy from major manufacturers. They then add other components to finish off the paint mix to customer specifications. Each of the four base mixes includes pigment, solvent and three additives. When Richelieu blends the four base mixes together, they want the final product to be within these specifications (these numbers are a percentage of total volume):

• ● Pigment: 25% ≤ x ≤ 30%

• ● Solvent: 60% ≤ x ≤ 65%

• ● Additive1:3%≤x≤5%

• ● Additive2:5%≤x≤7%

• ● Additive3:1%≤x≤3%

The specifications of each of the four base mixes before they are blended together is:

	Base 1	Base 2	Base 3	Base 4
Pigment Volume	30.0%	25.0%	25.0%	30.0%
Solvent Volume	48.0%	60.0%	67.5%	55.0%
Additive 1 Volume	10.0%	5.0%	0.0%	5.0%
Additive 2 Volume	6.0%	5.0%	2.0%	10.0%
Additive 3 Volume	6.0%	5.0%	5.5%	0.0%
Unit Cost	$15	$20	$25	$50

• ● Recommend what percentage of each base mix should be included in the blend to achieve specifications listed, keeping input costs as low as possible.

• ● Base mix 2 is purchased overseas and thus the price fluctuates due to currency exchange rates. Comment on how the percentage of each base included in the blend would change if the cost for mix 2 rises to $35 per unit and note what would happen to the total cost in this situation.

  Note: you do not need units of volume, use the percentages. The final ‘blend’ needs to include some percentage of each of the four base mixes, adding up to a total of 100%.

  Decision 4: Operations and Marketing - Product Mix

  Richelieu Specialty Paints has received a special order for two types of paints: Marine Coat, used on boats and Blocker, used on items that receive a great deal of strong, hot sun. Both paints use a UV blocking additive and a mold inhibitor. Richelieu currently has 240 litres of the mold inhibitor on hand and 300 litres of the UV blocking additive.

  The special-order customer has requested at least 200 cans of Marine Coat but will take up to 450 cans if available. The customer will take as much Blocker paint as Richelieu can provide.

  Amanda would like to generate the highest total contribution margin possible for this order and needs to know how much of each product should be made.

	Blocker	Marine Coat
Mold Inhibitor Used (litres per can)	0.4	0.6
UV Blocking Additive Used (litres per can)	1	0.5
Contribution Margin per can	$3.00	$6.00

Answer 1

The proper mix will be 60 Art websites ads,124 Social media ads,2 Art Tradeshow ads,12 Magazine ads.

Although 124.8 will be the optimal solution for social media ads we have to consider integer solutions since ads can not be a fraction.Also we can not take 125 ads to post on social media since then the total cost will be greater than the budget.

b.If we doubled the budget

The increased reach will be 60*15000+324*12000+2*5000+12*10000=4918000.

Here also we can not take fractional answes.Also we can not take 325 ads to post on social media since then the total cost will be greater than the budget.

The required dialogue box

Sorry I couldn't post all the answers,since we have a time limit. Please post the questions separetely as these are 4 separate problems of linear programming solving which is a lengthy process,If you have any problem understanding any part,leave a comment.I will try my best to help