Question A sportswear manufacturer is introducing a new line of sneakers. To introduce the new line, the company must pay out a
fixed cost of $1.5 million for advertising and equipment, plus there is a cost of 40 cents per pair of sneakers manufactured.
It plans to sell the sneakers for $75 per pair.
Let x be the number of pairs of sneakers manufactured. If the firm only manages to sell 15,000 sneakers, what is the total
loss?

  $381,000 loss

Step-by-step explanation:

Profit is the difference between revenue and cost. Cost is the sum of fixed cost and variable cost. Revenue is the product of selling price and quantity sold.

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If we assume the company only manufactures as many sneakers as it sells, then the profit can be found from ...

  R(x) = 75x . . . . . revenue from selling x sneakers

  C(x) = 1,500,000 +0.40x . . . . . . cost to manufacture x sneakers

  P(x) = R(x) -C(x) . . . . . profit from making and selling x sneakers

  P(x) = 75x -(1,500,000 +0.40x)

  P(x) = 74.60x -1,500,000 . . . . . profit from x sneakers

  P(15000) = 74.60·15,000 -1,500,000 = 1,119,000 -1,500,000

  P(15000) = -381,000

The total loss from making and selling 15,000 sneakers is $381,000.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3