Fred loves tomatoes.He makes soups,sauces,and stews with them; stuffs them; roasts them; and grills them.Fred has discovered a farmer's market where the price of a bushel of tomatoes depends on how many bushels are purchased.The first bushel is $15; the second,$12; the third,$10; and four or more,$9 each.Fred has $82 to spend on tomatoes and on "all other things" during the coming week.All other things sell for $1 per unit.Assume that all other things are measured on the vertical axis.What is the horizontal intercept of Fred's budget constraint?
A) 14.
B) 7.5.
C) 8.
D) 6.
E) 5.

Question

Quizplus · Accepted Answer

To find the horizontal intercept of Fred's budget constraint, we need to find the maximum number of bushels of tomatoes Fred can buy with his $82, assuming he spends all of his money on either tomatoes or all other things. Let x be the number of bushels of tomatoes Fred buys and y be the number of units of all other things he buys. Then, we can write the following equation for Fred's budget constraint:
15x + y = 82 (for the first bushel, Fred pays $15 and the rest of the money can be spent on all other things)
12x + y = 82 (for the second bushel, Fred pays $12 and the rest of the money can be spent on all other things)
10x + y = 82 (for the third bushel, Fred pays $10 and the rest of the money can be spent on all other things)
9x + y = 82 (for four or more bushels, Fred pays $9 per bushel and the rest of the money can be spent on all other things)
To find the maximum value of x, we need to find the intersection of the lines representing each of these equations. Solving the first two equations simultaneously, we get:
15x + y = 82
12x + y = 82
subtracting the second equation from the first gives
3x = 0, so x = 0. 
This means that the intersection of the first two lines is at (0,82), which represents the maximum amount of all other things Fred can buy if he doesn't buy any tomatoes (i.e. x = 0). 
Solving the second and third equations simultaneously, we get:
12x + y = 82
10x + y = 82
subtracting the second equation from the first, we get:
2x = 0, so x = 0.
This means that the intersection of the second and third lines is also at (0,82), which represents the maximum amount of all other things Fred can buy if he only buys up to two bushels of tomatoes. 
Finally, solving the third and fourth equations simultaneously, we get:
10x + y = 82
9x + y = 82
subtracting the second equation from the first, we get:
x = 1.
This means that the intersection of the third and fourth lines is at (1, 91), which represents the maximum amount of tomatoes and all other things Fred can buy with his $82. Therefore, the horizontal intercept is the value of x at this point, which is 8 (since Fred can only buy a whole number of bushels). So the answer is (C) 8 bushels of tomatoes.

Fred Loves Tomatoes