Question

Candy Kane Cosmetics (CKC) produces Leslie Perfume, which requires chemicals and labor. Two production processes are available: Process 1 transforms 1 unit of labor and 2 unites of chemicals into 3 oz of perfume. Process 2 transforms 2 units of labor and 3 units of chemicals into 5 oz of perfume. It costs CKC $3 to purchase a unit of labor and $2 to purchase a unit of chemicals. Each year, up to 20,000 units of labor and 35,000 units of chemicals can be purchased. In the absence of advertising, CKC believes it can sell 1,000 oz of perfume. To stimulate demand for Leslie Perfume, CKC can hire the lovely model Jenny Nelson. Jenny is paid $100/hour. Each hour Jenny works for the company is estimated to increase the demand for Leslie Perfume by 200 oz. Each ounce of Leslie Perfume sells for $5. Formulate a linear program to determine how CKC can maximize profits.

Answer 1

1. Divide the resources into three parts using the corresponding process 1, process 1, and process 2 formats to maximize the use of the resources.
2. Get the expected revenue by calculating the product of the total perfume in ounce and the price of an ounce of perfume.
3. Increase the advertisement hours of the product.
4. subtract the advert fee from the generated revenue to get the actual revenue.
5. subtract the cost of production from the actual revenue to get the actual profit.

Step-by-step explanation:

The get maximum profit, all the resources must be exhausted in production. The labor is divided into a ratio of 1:1:2 ( which is 5000, 5000, 1000), while the chemical units are in the ratio of 2:2:3 (10000,10000,15000). This would produce in each individual processes; 15000, 15000 and 25000 oz, which is a total of 55000 oz of perfume.

The expected revenue is $275000. If 1000oz from the 55000oz of perfume is sold without advertisement, model Jenny's awareness of the perfume increases the demand by 200oz per hour, therefore, 24hours would field 4800oz demanded, which would only take 270 hours to distribute all remaining perfumes.

The cost of production would be $130000 for labor and chemical resources plus the advert cost of $27000 ( 270 hours by 100) which is a total cost of $157000. The actual profit is $118000 ( $275000 - $157000).