To maximize the profit of the bakery, the first step is to findwhere the equatio
ID: 3088684 • Letter: T
Question
To maximize the profit of the bakery, the first step is to findwhere the equations for all of the constraints intersect.
Parts A and B might seem easy, but in them you will use thebasic techniques needed to solve any linear system: addingequations to cancel variables and substituting the value of onevariable to find the value of the other.
Suppose that a baker makes cakes andcookies. He knows that he is most efficient when he makes pairs ofcakes (instead of one cake at a time) or a dozen dozens of cookies.Call the number of pairs of cakes that he bakes in a week x and the number of grosses (dozens of dozens) of cookiesthat he bakes in a week y. There are two factors that limit how much he can bake in a week:He only wants to work for 40 {hours} a week and he only has one oven. Suppose that ittakes the baker 1 {hour} of prep time to make a pair of cakes or a gross ofcookies. Since he only wants to work 40 {hours} a week, his output of pairs of cakes x and his output of grosses of cookies y are constrained by the equation x + y = 40. To maximize the profit of the bakery, the first step is to findwhere the equations for all of the constraints intersect. Finding the minimumconstraints For the first part, you will look at x + y = 40 and y=0, which is also a constraint since the baker cannot make anegative number of cookies. Parts A and B might seem easy, but in them you will use thebasic techniques needed to solve any linear system: addingequations to cancel variables and substituting the value of onevariable to find the value of the other. Part A One way of solving systems of linearequations is by adding a multiple of one equation to the other. Themultiplier for one equation is chosen so that one of the twovariables will cancel out in the sum. What should you multiply theequation y=0 by so that when added to x + y = 40 the variable y will cancel out?Explanation / Answer
You don't actually have to multiply the equation y=0 byanything- in that form, it will substitute quite well into thex+y=40 equation. All you have to do now is substitute zeroin for y in the second equation, which will mean thatx is equal to 40. Hope that helps!
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