Web Mercantile sells many household products through an online catalog. The company needs substantial warehouse space for storing its goods. Plans now are being made for leasing warehouse storage space over the next 5 months. Just how much space will be required in each of these months is known. However since these space requirements are quite different, it may be most economical to lease only the amount needed to each month on a month by month basis. On the other hand the additional cost for leasing space for additional months is much less than for the first month, so it may be less expensive to lease the maximum amount needed for the entire 5 months. Another option is the intermediate approach of changing the total amount of space leased(by adding a new lease and/or having an old lease expire) at least once but not every month. The space requirement and the leasing costs for the various leasing periods are as follows:

Month Required space (Sq. Ft)

1 30,000
2 20,000
3 40,000
4 10,000
5 50,000

Leasing period(Months) Cost per Sq. Ft leased

1 $65
2 $100
3 $135
4 $160
5 $190

The objective is to minimize the total leasing cost for meeting the space requirements.

(A) Formulate a linear programming model for this problem
(B) Solve this model by the simplex method

Freese, inc., is in the process of preparing the fourth quarter budget for 2016, and the following data have been assembled: the company sells a single product at a price of $70 per unit. the estimated sales volume for the next six months is as follows: september 15,600 units october 14,400 units november 16,800 units december 24,000 units january 10,800 units february 12,000 units all sales are on account. the company's collection experience has been that 30% of a month's sales are collected in the month of sale, 68% are collected in the month following the sale, and 2% are uncollectible. it is expected that the net realizable value of accounts receivable (i.e., accounts receivable less allowance for uncollectible accounts) will be $396,032 on september 30, 2016. management's policy is to maintain ending finished goods inventory each month at a level equal to 30% of the next month's budgeted sales. the finished goods inventory on september 30, 2016, is expected to be 2,520 units. to make one unit of finished product, 6 pounds of materials are required. management's policy is to have enough materials on hand at the end of each month to equal 40% of the next month's estimated usage. the raw materials inventory is expected to be 21,168 pounds on september 30, 2016. the cost per pound of raw material is $5, and 70% of all purchases are paid for in the month of purchase; the remainder is paid in the following month. the accounts payable for raw material purchases is expected to be $79,758 on september 30, 2016. a. prepare a sales budget in units and dollars, by month and in total, for the fourth quarter (october, november, and december) of 2016.