please someone help me please. i have been stuck for hours. asap

Question

Question 1: A manufacturer makes two types of handmade fancy paper bags: type A and type B. Two designers—a cutter and a finisher—need to work on both kinds of bags. A type A bag requires 2 hours of the cutter's time and 1 hour of the finisher's time. A type B bag requires 1 hour of the cutter's time and 2 hours of the finisher's time. Each month the cutter is available for 104 hours and the finisher is available for 76 hours. The manufacturer gets a profit of $6 on each bag of type A and $11 on each bag of type B. Identify the number of bags of each type to be manufactured to obtain maximum profit.

A.) 44 bag A; 16 bag B

B.) 36 bag A; 32 bag B

C.) 32 bag A; 40 bag B

D.) 40 bag A; 20 bag B

Question 2: Lee spent $36 to purchase a combination of drinks, sandwiches, and chips for himself and his friends. A drink costs $2, a sandwich costs $4, and chips cost $0.50. Identify the linear equation that represents this situation.

A.) 2x + 4y + 0.5z = 36

B.) 2x − 4y + 0.5z = −36

C.) 2x + 4y −0.5z = 36

D.) 2x + 4y + 0.5z = −36

Question 2: Lisa purchased groceries worth $34 for a party. A gallon of milk costs $2.50, a gallon of ice cream costs $7.50, and a gallon of lemonade costs $3.00. If Lisa bought 4 gallons of milk, and 2 gallons of ice cream, how many gallons of lemonade did she buy?

A.) 2

B.) 3

C.) 4

D.) 5

Please just give explanation and solution.

Answer 1

1) For the first one, let's call the number of hours it takes to manufacture bag A as x, and the number of hours it takes to manufacture bag B as y. We know that the cutter is available for a maximum of 104 hours per month and the finisher 76 hours per month maximum. Since it takes the cutter 2 hours to manufacture bag A and one hour on bag B we get the equation 2x+y ≤ 104. Since it takes the finisher an hour for bag A and two hours on bag B, we get the equation x+2y ≤ 76, for similar reasons. Plugging in all the answers to the equations, the only answer that satisfies both of these conditions is A, so the answer is A.

2) If we let x, y, and z represent the cost of the drinks, sandwiches and chips respectively, the total cost is just the quantity of each item purchased multiplied by their cost. Since the chips cost 2 dollars, the sandwich costs 4 dollars and the chips cost 50 cents, and you have 36 dollars to play with, the only equation that makes sense is A.

3) If we let the gallons of milk be x, gallons of ice cream be y, and gallons of lemonade be z, the total cost is, again, just the quantity of each item multiplied by their price. Therefore, the linear equation for the cost would be 2.5x +7.5y +3z = 34. In this case, we are trying to find z, and we know that x = 4 and y = 2, since they purchased four gallons of milk and 2 gallons of ice cream. If we plug in the values for x and y, we get that (2.5)*4+(7.5)*2+3z = 34, which means 10+15+3z = 34, which means 25 +3z = 34, which means that 3z = 9, which finally implies z = 3 (which is B).