PaneraX Company prepares and delivers three kinds of breads - Whole Grain, Frenc
ID: 3011005 • Letter: P
Question
PaneraX Company prepares and delivers three kinds of breads - Whole Grain, French Baguette, Asiago Cheese- for their branches around the city. The beards are made early in the morning and are delivered the same day, and they are thrown away if not sold during the day they produced. It normally takes 0.5 minutes to make a Whole Grain, 1.2 minutes to make a French Baguette, and 0.8 minutes to make an Asiago Cheese. The profits gained from breads are $1.25, $2.00, and $1.75, respectively. PaneraX has 20 hours of labor available to produce the sandwiches each day. Based on its long-term performance, PaneraX estimates the demand for French Baguette to be at least as great as the demand for the two types of breads combined. Nevertheless, PaneraX has only enough materials to produce 500 French Baguette per day. Formulate an LP that helps the company maximize its profit. Solve the LP problem using the simplex method Formulate the dual for this problem and define the dual variables. Determine the optimal ranges for all three objective coefficients. Determine the sensitivity range for French Baguette demand constraint PaneraX is considering doing some marketing in its Asiago Cheese to boost demand. Based on its Analytics Team report, PaneraX estimates that spending $100 on some booklet that would be packaged with all other breads would increase the demand for both kinds of Whole Grain and Asiago Cheese by 200. Should the company make this expense?Explanation / Answer
a) Let the number of Whole Grain Bread be x
Let the number of French Baguette be y
Let the number of Asiago Cheese be z
Time constraint
0.5x + 1.2y + 0.8z <= 1200
Profit Function: z = 1.25x + 2y + 1.75z
y >= (x+z)
y <= 500
b)
y will be 500, since y >= (x+z), hence the value of z must be made 500 in order to increase profit
But it should satisfy the time constaint
Checking time constraint
500 * 1.2 + 500 * 0.8 < 1200
1000 < 1200
Hence Profit Function = 500 * 2 + 500 * 1.75 = 500 * 3.75 = 1875$
d) 0<=y<=500
0<=(x+z)<=500
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.