Question

The price-demand and cost functions for the production of microwaves are given asp= 250 - q/40 and C(q) = 90000 + 80q,where q is the number of microwaves that can be sold at a price of p dollars per unit and C(q) is the total cost (in dollars) of producing q units.(D) Evaluate the marginal revenue function at q=1100.R'(1100) =

Answer 1

Let's first determine the equation for marginal revenue, R'(q).

`\text{ Revenue = No. of microwaves x Price = \lparen q\rparen\lparen250 - q/40\rparen}`
`\text{ R\lparen q\rparen= 250q - }\frac{\text{ q}^2}{40}`
`\text{ R'\lparen q\rparen= 250\lparen1\rparen- }\frac{\text{q\lparen2\rparen}}{\text{40}}`
`\text{ R'\lparen q\rparen= 250 - }\frac{\text{q}}{20}`

Let's now determine the marginal revenue at q = 1,100.

`\text{ R'\lparen q\rparen= 250 - }(1,100)/(20)\text{ = 250 - 55}`
`\text{ R'\lparen q\rparen= 195}`

Therefore, R'(1,100) = 195

The answer is 195