(a) A store is considering how many current model televisions to order given a new model is soon to be released next month. The probability distribution of demand for the current model of television is normal with a mean of 350 units and a standard deviation of 100. The current television retails for $1500 each and costs $750 each to purchase. The total cost of a shortage is estimated to be $80 per television. Any unsold televisions at the end of the month will be sold in store at the discounted price of $650 per television. (i) How many current televisions should be ordered to minimise the expected total cost given that only one order may be placed? (5 marks) 5 (ii) The supplier is offering an order of 310 units of the soon-to-be-obsolete model at a reduced purchase price of $700. Any unsold televisions cannot be sold in store but must instead be disposed of at a cost $50 per television. If the shortage cost remains the same, what retail price per television will make the 310 units optimal? (5 marks) (b) The demand for gourmet chocolate cakes sold by a local bakery is estimated to follow an expo- nential distribution with a mean of 130 cakes 90 , I > 0 f(x) = 0 otherwise. Each chocolate cake costs the owner of the bakery $10 to bake and are sold for $20 per cake. If a customer arrives in the bakery to buy a chocolate cake, and none is available, the owner gives the customer a discount voucher costing $10 as a goodwill gesture. Any gourmet chocolate cakes left over at the end of the week can be sold for $5 per cake. 1.30 e 2 (i) How many gourmet chocolate cakes should the bakery bake for sale? (5 marks) (ii) If gourmet chocolate cakes left over at the end of the week cannot be sold, but instead must be disposed of at a cost of $7.50 per cake, how many gourmet chocolate cakes should instead be baked for sale