A popular Singapore based Department store sells exotic leather handbags imported from

Australia. In the spring of each year, the company must decide on the number of each

style of leather handbags to order from their supplier for the upcoming winter season.

For a particular line of such handbags for women, the supplier's price is $$140$ and the

retail selling price is $$210.$

The company estimates their expected sales to be $100$ such handbags, but with

considerable uncertainty, which their marketing people have expressed as a Normal

distribution with a standard deviation of $30.$

Any handbags not sold by the end of winter selling season are sold to a discount store

$($such as Simply Warehouse$)$ at a unit price of $$120.$ The supplier in Australia incurs a

shipping cost of $$500$ for each shipment it makes to the department store in Singapore; its

own purchase price $($from the handbag manufacturer$)$ is $$80$ a bag.

$($a$)$ How many handbags should the company order?

marks$)$

$($b$)$ Assuming the Department store decides to order a quantity equal to their expected demand,

what is the resulting profit for them and their supplier?

$(5$ marks$)$

$($c$)$ To encourage the Department store to place larger orders the Australian supplier proposes

a revenue$-$sharing arrangement, offering a lower wholesale price, but with $20\%$ of sales

revenue to be shared with the supplier, if the customer orders $150$ handbags. What

wholesale price should the supplier offer to the customer to ensure its own profit stays the

same as before, assuming the department store's sales remain the same? For this new

wholesale price, what would be the Department store's profit? Would the Department

Store accept this contract at the current level of sales?