Ordering Stock for ProductPusher
An important part of your duties as manager is to determine how much of each product to order for ProductPusher's monthly stock inventory. You first priority is to focus on your three most recently acquired products, with the aim to maximise ProductPusher's profit. The first product is the cosmetic set BlissBeauty that generates $130 in profit and is overwhelmingly popular with female shoppers up to the age of 34. Due to a current manufacturing shortage crisis however, you are only able to order up to 35 sets per month. Orange's new netbook, the oNetbook, is another high seller which costs ProductPusher only $110 to purchase yet retails at the bargain price of $385.
The third product is the box set Fragrance by Deckham, the latest fragrance from the English soccer superstar B. Deckham. The fragrance costs ProductPusher $8.50 to purchase (per box set) and retails on ProductPusher's website for $133.50 (per box set).
After reviewing the profit/loss sheets from the previous financial quarter, ProductPusher has decided to spend no more than $5800.00 per month to acquire these products. Of this amount, a maximum budget of $4,300.00 has been allocated to purchasing the products, and the remaining maximum monthly budget is to be spent on shipping the products from the suppliers to ProductPusher's storage warehouse. The shipping cost of the B. Deckham fragrance is $11.25 per box set, while the oNetbook shipping cost is $18.50 per computer, which includes a shipping insurance plan of $12.00. It was also determined that a maximum of 45 oNetbooks should be purchased from the supplier per month, to avoid an unacceptable increase in shipping costs. Finally, as ProductPusher order regularly from BlissBeauty Manufacturing, they have been offered a 15% reduction in cost price of the BlissBeauty cosmetic sets, and now pay the manufacturers $11.50 per set, with shipping costs set at $8.50 per set.
Modelling Approach: You decide to use linear programming to solve this problem.
ld not write more than 4 paragraphs. Alternatively, bullet point format reporting is acceptable and encouraged to facilitate report readability:
a. Explain the purpose of Managerial Decision II. Then, explain the optimal number of BlissBeauty cosmetic sets, oNetbooks and B. Deckham box sets to be ordered and sold, and the maximum profit in the coming month.
b. The actual total amounts spent on shipping and purchasing the products from the manufacturers.
c. Your concerns from part (iii), and its impact on the solution to the linear programming problem.
d. The potential implications on the profit if you double the number of BlissBeauty cosmetic sets ordered, once the manufacturing shortage crisis is over. Also include the maximum possible number of BlissBeauty cosmetic sets you can order, without changing the optimality of the solution obtained in (ii).