Respuesta :
Answer:
Jack and Jill must sell 10 systems each of PS4 and X-box One
Step-by-step explanation:
Solution:-
- The profit on Xbox One system, p1 = $100
- The profit on PS4 system, p2 = $80
- The number of systems shipped this week, N = 20
- The number of PS4 systems sold, n2 ≥ 10
- The number of Xbox One systems sold, n1 ≥ 8
- We are to maximize the total profit ( P ) for jack jill. The total profit made by Jack and jill will depend on the number of each system sold multiplied with their respective profits per system.
- We will mathematically express the total profit:
P = n1*p1 + n2*p2 ..... Eq 1
Where,
- The total number of systems shipped are ( N ):
N = n1 + n2
20 = n1 + n2
- Develop an expression relating n1 and n2:
n1 = 20 - n2 .... Eq2
- Substitute Eq2 into Eq1:
P = ( 20 - n2 )*100 + n2*80
P = 2000 - 100*n2 + 80*n2
- To maximize the total profit ( P ) we need to set the first derivative of P with respect to number of PS4 system sold ( n2 ) to zero and determine the maximizing value of ( n2 ):
P = 2000 - 20*n2
- The range of number of PS4 systems to be sold is n2 ≥ 10. But from the profit function we see that number of PS4 systems sold must be small as possible. Hence, the lowest value for n2 = 10.
Hence,
- The number of X-box systems sold n1 would be:
n1 = 20 - 10
n1 = 10
Answer: Jack and Jill must sell 10 systems each of PS4 and X-box One.
