Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly costs of $70,000 just to keep the place running. On top of that, your regular cabaret artist is charging you $5000 per performance, and your jazz ensemble is charging $900 per hour. Set up a (monthly) cost function for the scenario. (Let C represent the monthly cost in dollars, x represent the number of performances by the cabaret artist per month and y represent the number of hours of jazz per month.

C = 70000 + 5000x + 900y

Step-by-step explanation:

You are paying

- $70,000 to keep the place running,

- $5000 to cabaret artist per performance, since x represents the number of performances by the cabaret artist per month, it is 5000x in a month

- $900 to jazz ensemble per hour, since y represents the number of hours of jazz per month, it is 900y in a month.

If you sum all the costs and set it to the C, you will get:

C = 70000 + 5000x + 900y

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204