1) Bacteria of species A and species B are kept in a single test tube, where the

Question

1) Bacteria of species A and species B are kept in a single test tube, where they are fed two nutrients. Each day the test tube is supplied with 19,680 units of the first nutrient and31,630 units of the second nutrient. Each bacterium of species A requires 4 units of the first nutrient and 5 units of the second, and each bacterium of species B requires 1 unit of the first nutrient and 6 units of the second. What populations of each species can coexist in the test tube so that all the nutrients are consumed each day?

2) A company charting its profits notices that the relationship between the number of units sold, x, and the profit, P, is linear. If 190 units sold results in $2380 profit and 240 units sold results in $4980 profit, write the profit function for this company.
P =  

Find the marginal profit.
$

3) A company distributes college logo sweatshirts and sells them for $45 each. The total cost function is linear, and the total cost for 90 sweatshirts is $4236, whereas the total cost for200 sweatshirts is $5776.(a) Write the equation for the revenue function R(x).
R(x) =

(b) Write the equation for the total cost function C(x).
C(x) =  

(c) Find the break-even quantity.
x = sweatshirts

Explanation / Answer

It's given that the relation between the number of units sold and the profit is linear.

1. 190 unit sold in $2380

2. 240 unit sold in $4980

Now

linear relation between units sold and profit will be given by

P = m*x + b

x = units sold

2380 = m*190 + b

4980= m*240 + b

Solving both equations:

4980 = m*240 + 2380 - m*190

2600 = m*50

m = 52

b = 2380 - 52*190 = -7500

So profit function will be

P = 52*x - 7500

marginal profit is given by the value of m

marginal profit = $52 per unit

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.