?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 thecompany
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 andDesign. The company was founded by Amanda’s father and he recentlyasked her to take over managing it so that he could retire. Amandaagreed and left her interior design job with an architecture firmto assume the role. She is keen to develop the businessfurther.
The company makes a wide variety of paints, mostly targeted atfine artists. However, since Amanda has had experience in interiordesign she has determined that the company could apply its skillsto develop new products for that industry and others.
She knows that she hasn’t yet developed her quantitativeanalysis skills to the point they need to be to run a company, soshe is seeking assistance with four decisions that she needs tomake. She would like to have a report from you providingrecommendations for each decision, along with the backgroundcalculations 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 customersthat see her company’s ads or other marketing efforts).
She is considering a mix of placing ads on art websites and inprinted art magazines, as well as using targeted social media adplacements and appearances at art tradeshows. She wants to makesure that the company has an online presence, so would like to seeat least 100 ads placed in any combination of websites and socialmedia per year. However, she has data that suggests that if sheadvertises on the websites more than 60 times per year she will bewasting money. There are seven art tradeshows that the companycould attend, but Amanda feels it is mandatory to attend at leastthe two most popular tradeshows. There are three major artmagazines, each published monthly, that Amanda would like toadvertise in. She could advertise in each of these once per monthbut would be comfortable reducing the frequency to a minimum ofonce every three months in each magazine and rotating theplacements between the magazines.
The reach and cost of each type of ad placement or event isshown 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 promotionsfor the company.
? Also comment on what would change if Amanda doubled heradvertising and promotions
budget. Estimate the increased reach if the budget were todouble.
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 havedeveloped four potential investments in addition to leaving thecash in a low interest deposit. The four new opportunities are:
1. Purchase some shares of a major supplier (25% risk of totalloss, 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 oftotal loss, 3% expected return)
Leaving the money in a low interest deposit is virtuallyriskless and has a 0.5% return.
Richelieu’s father had provided Amanda with some guidelines forinvestment, aimed at diversification and risk management. Theseare:
Invest a maximum of 40% of the total cash in any one of the fournew opportunities to ensure some risk control.
Invest at least $100,000 in each of the four new opportunitiesto ensure some diversity.
Limit the total potential loss to $300,000, based on the riskfactors indicated.
Ensure the highest return possible.
? Recommend how much money should be invested in each of thefour new investments, as well as the low interest deposit.
? Also, comment on how this mix would change, and what wouldhappen to potential return, if Amanda decided to take a moreconservative approach and limit the total potential loss to$150,000.
Decision 3: Operations - Materials Blending
Richelieu Specialty Paints has begun making paints for theinterior design market. The company starts the process by blendingfour base paint mixes together that they buy from majormanufacturers. They then add other components to finish off thepaint mix to customer specifications. Each of the four base mixesincludes pigment, solvent and three additives. When Richelieublends the four base mixes together, they want the final product tobe within these specifications (these numbers are a percentage oftotal 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 theyare 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 includedin the blend to achieve specifications listed, keeping input costsas low as possible.
? Base mix 2 is purchased overseas and thus the price fluctuatesdue to currency exchange rates. Comment on how the percentage ofeach base included in the blend would change if the cost for mix 2rises to $35 per unit and note what would happen to the total costin this situation.
Note: you do not need units of volume, use the percentages. Thefinal ‘blend’ needs to include some percentage of each of the fourbase mixes, adding up to a total of 100%.
Decision 4: Operations and Marketing - Product Mix
Richelieu Specialty Paints has received a special order for twotypes of paints: Marine Coat, used on boats and Blocker, used onitems that receive a great deal of strong, hot sun. Both paints usea UV blocking additive and a mold inhibitor. Richelieu currentlyhas 240 litres of the mold inhibitor on hand and 300 litres of theUV blocking additive.
The special-order customer has requested at least 200 cans ofMarine Coat but will take up to 450 cans if available. The customerwill take as much Blocker paint as Richelieu can provide.
Amanda would like to generate the highest total contributionmargin possible for this order and needs to know how much of eachproduct 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 |
