You are the manager of two plants (factories) in Mexico that manufacture shoes. The combined monthly output of both plants is to be 10,000 pairs of shoes. How you would best divide this output of 10,000 pairs of shoes between the two plants. You may make your arguments in words with the aid of diagrams, i. e., without the use of math. On the other hand, if you are comfortable with math (calculus), the following additional information may be made use of by you. The cost function of Plant 1 is C1 = a1Q1 + a2Q12 + Q13and that of Plant 2 is C2 = b1Q2 + b2Q22 + Q23, where Q1 and Q2 denote, respectively, the outputs of Plant 1 and Plant 2.

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.