A farmer can buy four types of plant food. Each barrel of mix A contains 40 pounds of phosphoric acid, 55 pounds of nitrogen, and 30 pounds of potash; each barrel of mix B contains 25 pounds of phosphoric acid, 70 pounds of nitrogen, and 20 pounds of potash; each barrel of mix C contains 30 pounds of phosphoric acid, 25 pounds of nitrogen, and 20 pounds of potash; each barrel of mix D contains 75 pounds of phosphoric acid, 35 pounds of nitrogen, and 50 pounds of potash. Soil tests indicate that a particular field needs 1,190 pounds of phosphoric acid, 880 pounds of nitrogen, and 810 pounds of potash. There are multiple solutions to the number of barrels of each type of food that could be mixed together to supply the necessary nutrients for the field. The solutions can be expressed as (13t) barrels of mix A, (t8) barrels of mix B, (292t) barrels of mix C, and t barrels of mix D, where t is an integer satisfying 8t13.

The costs of the four mixes are Mix A, $38, Mix B, $73,

Mix C, $53, Mix D, $62. Which of the solutions to the problem of supplying the correct nutrients would minimize the cost of the plant food?

Let the variables x1 represent the number of barrels of mixture A, x2 represent the number of barrels of mixture B, x3 represent the number of barrels of mixture C and x4 represent the number of barrels of mixture

D. Write the equation that can be used to find the cost C in terms of the variables x1 through

x4.

_____

(Do not include the $ symbol in your answer.)

The minimum cost is achieved by purchasing ____ barrel(s) of mix A,______ barrel(s) of mix B,

______ barrel(s) of mix C, and _____ barrel(s) of mix D.