Astore sells two types of toys, a and b. the store owner pays $8 and $14 for each one unit of toy a and b respectively. one unit of toys a yields a profit of $2 while a unit of toys b yields a profit of $3. the store owner estimates that no more than 2000 toys will be sold every month and he does not plan to invest more than $20,000 in inventory of these toys. how many units of each type of toys should be stocked in order to maximize his monthly total profit?

A = 1333 and B = 667

Step-by-step explanation:

Given that a store sells two types of toys, A and B.

      AB

cost       814

Profit23

Objective is to maximize profit

where A = no of toys of A and B = no of toys of B

Constraints are

By solving this equation, we get

(A,B)= (1333,667)

Corner points would be lowest of x and y intercepts in both

(A,B) = (2000,0) and (0,1428)

Profit for

Profit for

Profit for

Since maximum at (1333,667) we find that

to maximize profit A = 1333 and B = 667 to be produced.

12 do both hurdles and long jump

Step-by-step explanation:

3/8 of the team does hurdles, so that number is 3/8·40 = 15.

Of those 15, 4/5 do long jump, so there are ...

4/5·15 = 12 . . . hurdlers who do long jump