Solve the below by writing a linear program and then solving that linear program with whatever method you prefer.

Suppose that you are given two different types of concrete. The first type contains 30% cement, 40% gravel, and 30% sand (all percentages by weight). The second type contains 10% cement, 20% gravel and, 70% sand. The first type of concrete costs $5 per pound and the second type costs $1 per pound. How many pounds of each type of concrete should you buy and mix together so that your cost is minimized but you get a concrete mixture that has at least a total of 5 pounds of cement, 3 pounds of gravel, and 4 pounds of sand? What is the total cost?

Type 1: ______ lbs
Type 2: ______ lbs
Cost: _______ dollars