Tonya's budget constraint for gallons of gasoline (G)and shirts (S)each month can be expressed by the equation G = 100 - 2S,where G is the number of gallons of gasoline she buys and S is the total number of shirts she buys.Assume that she spends her entire budget each month.If the price of shirts is $10,which consumption bundle lies INSIDE Tonya's budget line?
A)45 shirts and 100 gallons of gasoline
B)50 shirts and 0 gallons of gasoline
C)0 shirts and 100 gallons of gasoline
D)10 shirts and 5 gallons of gasoline

Question

Quizplus · Accepted Answer

To determine which consumption bundle lies inside Tonya's budget line, we need to consider the total expenditure on gasoline and shirts. Since Tonya spends her entire budget each month, we know that her expenditure on gasoline (P_G x G) plus her expenditure on shirts (P_S x S) must equal her total budget.

Substituting G = 100 - 2S and P_S = $10, we can rewrite the budget constraint as:

P_G x (100 - 2S) + P_S x S = B

where B is Tonya's budget.

Simplifying this equation, we get:

P_G x 100 - (P_G + P_S) x S = B

Since the prices of gasoline and shirts are positive, the slope of Tonya's budget line is negative. In other words, if she buys more gasoline, she has less money left over to buy shirts, and vice versa.

Now, let's consider each option:

A) 45 shirts and 100 gallons of gasoline

If Tonya buys 45 shirts, her expenditure on shirts is P_S x S = $10 x 45 = $450. Substituting G = 100 - 2S, her expenditure on gasoline is:

P_G x G = P_G x (100 - 2S) = P_G x 100 - 2P_G x S

If we assume that P_G is greater than $2.25 (i.e. her expenditure on gasoline is at least $225), then her total expenditure exceeds her budget.

Therefore, option A is not feasible.

B) 50 shirts and 0 gallons of gasoline

If Tonya buys 50 shirts, her expenditure on shirts is P_S x S = $10 x 50 = $500. Since she buys no gasoline (i.e. G = 0), her total expenditure is $500, which is within her budget.

Therefore, option B is feasible and lies inside Tonya's budget line.

C) 0 shirts and 100 gallons of gasoline

If Tonya buys no shirts (i.e. S = 0), her expenditure on shirts is zero. Substituting G = 100 - 2S, her expenditure on gasoline is:

P_G x G = P_G x 100

If we assume that P_G is greater than $5 (i.e. her expenditure on gasoline is at least $500), then her total expenditure exceeds her budget.

Therefore, option C is not feasible.

D) 10 shirts and 5 gallons of gasoline

If Tonya buys 10 shirts, her expenditure on shirts is P_S x S = $10 x 10 = $100. Substituting G = 100 - 2S, her expenditure on gasoline is:

P_G x G = P_G x (100 - 2S) = P_G x 80

If we assume that P_G is greater than $6.25 (i.e. her expenditure on gasoline is at least $500), then her total expenditure exceeds her budget.

Therefore, option D is not feasible.

In summary, the only feasible consumption bundle that lies inside Tonya's budget line is option B: 50 shirts and 0 gallons of gasoline.

Tonya's Budget Constraint for Gallons of Gasoline (G)and Shirts (S)each