Bravura Cosmetics (BC) produces Kaya Rose Perfume, which requires chemicals and
ID: 2486183 • Letter: B
Question
Bravura Cosmetics (BC) produces Kaya Rose Perfume, which requires chemicals and labor. Two production processes are available. Process 1 transforms 1 unit of labor and 2 units of chemicals into 3 ounces of perfume. Process 2 transforms 2 units of labor and 3 units of chemicals into 5 ounces of perfume. It costs BC $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, BC believes it can sell 1000 ounces of perfume. To stimulate demand for Kaya Rose, BC can hire the lovely model Harriet Hauch Harriet is paid $100 per hour. Each hour Harriet works for the company is estimated to increase the demand for Kaya Rose Perfume by 200 ounces. Each ounce of Kaya Rose Perfume sells for $5. Determine how BC can maximize its profit.Explanation / Answer
1 unit of labour=3 20000 units 1 unit of chemical= 2 35000 units maximum sales= 1000 units Maximum sales= 1200 units Process with (Hire Harriet) with 1 unit of labour=100 Process-1 Process-2 Process-1 Process-2 Labour: 1 unit Labour: 2 units Labour: 1 unit Labour: 2 units Chemical: 2 units Chemical: 3 units Chemical: 2 units Chemical: 3 units Output: 3 units Output: 5 units Output: 3 units Output: 5 units selling price=5 per ounce selling price=5 per ounce Sales=1000 units Sales=1000 units Output=1000/3=333.33 Output= 1000/5=200 Let number of hours worked by harriet= x Labour= 333.33 units Labour=200*2=400 units Chemical=200 x *2/3 200x*2/3 = 35000 Chemical=2*333.33=666.66 units Chemical=200*3=600 units labour=200 X units X=262.5 units Output=3*333.33=1000 ounces Output=200*5=1000 onces Output=x *200 oounce 200 x = 20000 sales revenue: 1000*5=5000 sales revenue: 1000*5=5000 X = 100 less: labour=333.33*3=1000 less: labour=200*3=600 X =262.5 or 100 which ever is less chemical=666.66*2=1333.32 chemical=200*2=400 X=100 Revenue= $2666.68 Revenue= $4000 Chemical=200*100*2/3=13333.33 labour=200*100=20000 Output=200*100=20,000 ounce Sales: 20,000*5=100000 less: 20000*100=2000000 this results in loss hence it is advised not to hire Harriet