# Mat 540 week 6 homework 1

1.      A Cereal Posse makes a cereal from divers ingredients. Two of the ingredients, oats and rice, furnish vitamins A and B. The posse wants to apprehend how numerous ounces of oats and rice it should enclose in each box of cereal to converge the poverty requirements of 45 milligrams of vitamin A and 13 milligrams of vitamin B while minimizing require. An ounce of oats contributes 10 milligrams of vitamin A and 2 milligram of vitamin B, forasmuch-as an ounce of rice contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats requires \$0.06, and an ounce of rice requires \$0.03.

a. Formulate a rectirectidirect programming copy for this amount.

b. Solve the copy by using graphical separation.

2.      A Furniture Posse consequences chairs and boards from two resources- strive and forest. The posse has 125 hours of strive and 45 board-ft. of forest suited each day. Demand for chairs is poor to 5 per day. Each chair requires 7 hours of strive and 3.5 board-ft. of forest, forasmuch-as a board requires 14 hours of strive and 7 board-ft. of forest. The gain ascititious from each chair is \$325 and from each board, \$120. The posse wants to designate the compute of chairs and boards to consequence each day in regulate to maximize gain. Formulate a rectirectidirect programming copy for this amount.

a. Formulate a rectirectidirect programming copy for this amount.

b. Solve the copy by using graphical separation (Do not rotund the answers)

c. How plenteous strive and forest accomplish be unused if the optimal computes of chairs and boards are consequenced?

3.      Kroeger supermarket sells its own disgrace of canned peas as courteous as divers generally-known disgraces. The fund makes a gain of \$0.28 per can for its own peas and a gain of \$0.19 for any of the generally-known disgraces. The fund has 6 balance feet of rejection extension suited for canned peas, and each can of peas takes up 9 balance inches of that extension. Point-of-sale records semblance that each week the fund never sales over than half as numerous cans of its own disgrace as it does of the generally-known disgraces. The fund wants to apprehend how numerous cans of its own disgrace of peas of peas and how numerous cans of the generally-known disgraces to fund each week on the allocated rejection extension in regulate to maximize gain.

a. Formulate a rectirectidirect programming copy for this amount.

b. Solve the copy by using graphical separation