Suppose that a lumberyard has a supply of 10-ft boards, which are cut into 3-ft, 4-ft, and 5-ft boards according to customer demand. The 10-ft boards can be cut into several sensible patterns. each in such a way that there the leftover material is less than 3-ft. The lumberyard just received an order for 90 3-ft boards, 60 4-ft boards. and 60 5-ft boards.

a. Determine all sensible patterns the lumberyard may use to cut the 10-ft boards.
b. The lumberyard would like to use as few 10-ft boards as possible in meeting the demand. Write out a mathematical formulation for the problem as an integer linear program ILP), and setup/solve this problem using Microsoft Excel solver. What is the optimal number of each pattern, and what is the minimum number of boards to cut?

What are the period and vertical shift of the cosecant function below? period: ; vertical shift: 1 unit up period: ; vertical shift: 2 units up period: ; vertical shift: 1 unit up period: ; vertical shift: 2 units up?

Paid-in-capital in excess of par represents the amount of proceeds a. from the original sale of common stock b. in excess of the par value from the original sale of common stock c. at the current market value of the common stock d. at the curent book value of the common stock

Selected t-account balances for bloomfield company are shown below as of january 31, which reflect its accounting adjustments. the firm uses a calendar-year accounting period, but prepares monthly accounting adjustments.suppliesjan. 31 bal. 1,800 1,800 jan. 31 bal.supplies expensejan. 31 bal. 1,920 1,148 jan. 31 bal.prepaid insurancejan. 31 bal. 1,148 1,148 jan. 31 bal.insurance expensejan. 31 bal. 164 164 jan. 31 bal.wages payablejan. 31 bal. 1,400 1,400 jan. 31 bal.wages expensejan. 31 bal. 6,400 6,400 jan. 31 bal.truckjan. 31 bal. 17,376 17,376 jan. 31 bal.accumulated depreciation -truckjan. 31 bal. 5,068 5,068 jan. 31 bal.a. if the amount in supplies expense represents the january 31 adjustment for the supplies used in january, and $1,240 worth of supplies were purchased during january, what was the january 1 beginning balance of supplies? $answerb. the amount in the insurance expense account represents the adjustment made at january 31 for january insurance expense. if the original insurance premium was for one year, what was the amount of the premium, and on what date did the insurance policy start? amount of the premium $answerthe policy began on answerjune 1july 1august 1september 1october 1november 1 of the previous year.c. if we assume that no beginning balance existed in either in either wage payable or wage expense on january 1, how much cash was paid as wages during january? $answerd. if the truck has a useful life of four years (or 48 months), what is the monthly amount of depreciation expense, and how many months has bloomfield owned the truck? answermonths