1) Manager of the large apartment complex knows from experience that 120 units will be occupied if rent is 342 dollars per month. Market survey recommends that, on average, one extra unit will remain vacant for each 9 dollar increase in rent. One extra unit will be occupied for every 9 dollar decrease in rent. What rent must manager charge to maximize revenue? _____________
2) The manufacture has been selling 1850 television sets a week at $480 each. Market survey signifies that for each $15 rebate offered to the buyer, number of sets sold will increase by 150 per week.
a) Compute function representing demand p(x), where x is number of television sets sold per week and p(x) is corresponding price.
b) How large rebate must company offer to the buyer, to maximize its revenue?
c) If weekly cost function is 148000+160x, how must it set size of rebate to maximize its profit?
3) Showroom manager of the dealership knows that they will sell 320 mopeds over course of the complete year. Their cost to store the moped for the entire year is $12. To reorder mopeds from their supplier, there is fixed reordering cost of $30 and a $5 handling charge for every moped ordered. How frequently must manager order mopeds, and in what lot size, to minimize inventory costs?
For the lot size x, total inventory cost for the year is given by function:
Determine what lot size will minimize inventory costs?
How many times during year must manager reorder mopeds?