You decide to make and sell two different gift baskets at your local outdoor market. Basket A contains 3 cookies, 6 chocolates, and 2 jars of jam and makes a profit of $12. Basket B contains 6 cookies, 3 chocolates, and 2 jars of jam and makes a profit of $15. You have just made 48 cookies, 36 chocolates, and 18 jars of jam. How many of each type of gift basket should you make to maximize the profit? a) State what you assign to x and y. Write the objective function. b) Write the three constraint inequalities. c) Find the axes intercepts of each of the above inequalities.

You decide to make and sell two different gift baskets at your local outdoor market. Basket A contains 3 cookies, 6 chocolates, and 2 jars of jam and makes a profit of $12. Basket B contains 6 cookies, 3 chocolates, and 2 jars of jam and makes a profit of $15. You have just made 48 cookies, 36 chocolates, and 18 jars of jam. How many of each type of gift basket should you make to maximize the profit? a) State what you assign to x and y. Write the objective function. b) Write the three constraint inequalities. c) Find the axes intercepts of each of the above inequalities.

Question
You decide to make and sell two different gift baskets at your local outdoor market. Basket A contains 3 cookies, 6 chocolates, and 2 jars of jam and makes a profit of $12. Basket B contains 6 cookies, 3 chocolates, and 2 jars of jam and makes a profit of $15. You have just made 48 cookies, 36 chocolates, and 18 jars of jam. How many of each type of gift basket should you make to maximize the profit? a) State what you assign to x and y. Write the objective function. b) Write the three constraint inequalities. c) Find the axes intercepts of each of the above inequalities.

Answers (1)

2020-11-02
For part (a) it is required to assign x and y and write the objective function. Let x be the number of gift Basket A purchased and y be the number of gift Basket B purchased. The objective function of the given information is: objective function: maxmize z = 12x+15y For part (b) it is required to write the constraints inequality. Constraints are: 3x+6y <= 45 rArr x+2y<=16 6x+3y<=36 rArr 2x+y<=12 2x+2y<=18 rArr x+y<=9 For part (c) It is required to find the intercepts of each inequalities. x+2y<=16 x/16 + (2y)/16 <= 1 rArr x/6 + y/12 <= 1 intercept of the above inequality is (16,0) and (0,8) 2x+y<=12 (2x)/12+y/12<=1 rArr x/6+y/12<=1 x/16 + (2y)/16 <= 1 rArr x/6 + y/12 <= 1 intercept of the above inequality is (6,0) and (0,12) x+y<=9 x/9+y/9<=1 intercept of the above inequality is (9,0) and (0,9)
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