Why does Mary make the officers eat the lamb in "Lamb to the Slaughter"?

Mary doesn't force the police officers to eat the leg of lamb she's prepared, but she does encourage it. It smells good, they don't suspect her of the crime, and they are hungry after a long day. The text states,

"Please," she begged. "Personally, I couldn't eat a thing, but it'd be a favor to me if you ate it up. Then you can go on with your work."

The detectives hesitated, but they were hungry, and in the end, they went into the kitchen and helped themselves to supper.

Unbeknownst to the officers, though known to Mary and to us as readers, Mary recently used the frozen leg of lamb they are eating to murder her husband by whacking him on the back of the head with it. They don't suspect her because she is the wife of a fellow officer: to them, she is a social acquaintance rather than a potential murderer. She also looks like a gentle lamb rather than a killer. She is heavily pregnant with a calm demeanor and big, dark eyes.

Mary encourages them to eat the leg of lamb so she can get rid of the murder weapon, which is the piece of evidence that links her to the crime. This is an example of dramatic irony because we as the audience know that the police are eating the evidence while they do not suspect a thing. Mary also seems to get a special enjoyment out of tricking the police this way, as at the end of the story, we learn that she begins to laugh.

In "Lamb to the Slaughter," why does Mary insist the policeman eat the leg of mutton?

Mary insists upon this because the leg of mutton is what she used to kill her husband Patrick. Therefore the policemen will unknowingly destroy a vital piece of evidence that could have implicated her. The scene is a piece of consummate black comedy, of the kind that Dahl is famed for; a bunch of policemen sit and unknowingly eat a murder weapon.

The absurd humour of the situation is not lost on Mary as she listens to the policemen from another room, discussing the club that they think must have been used to kill Patrick:

'Personally, I think it's right here on the premises.'

'Probably right under our very noses. What do you think, Jack?'

And, in the other room, Mary Maloney began to giggle.

As in so many of his stories, for both adults and children, Dahl indulges in a bizarre and grotesque twist that completely upends a seemingly normal situation. Earlier, we have a serene domestic picture of Mary as a devoted wife waiting for her husband to come home from work. Then the sense of peace is shattered when he arrives only to tell her he’s leaving her, and she wastes no time in getting her revenge when she uses the frozen leg of lamb that they were going to have for dinner, to smash his head in. Therefore a seemingly innocent everyday item is transformed into something lethal; and Mary, a seemingly ordinary housewife, in an instant becomes a murderess, a fearsome avenger. Moreover, she manages to completely deceive the police.

Dahl also twists the meaning of a common phrase to use as the title of the story. The image of the lamb suggests innocence and purity; 'lamb to the slaughter’ normally means someone innocent who is about to be hurt in some way. The title could refer to Patrick, as he is the one who is killed, although he is not as innocent as the image of the lamb would suggest; he is planning to desert his wife, and tells her so in rather callous and abrupt manner.

The image of the lamb could also conceivably refer to Mary herself, as she appears very much a sweet, innocent type at first; but she commits slaughter, and in so doing, her own former innocence and goodness is sacrificed. 

Finally, the title could also be taken in a literal sense, which plays upon the irony of a lamb (or a piece of it) actually becoming the instrument of slaughter for once.

What are Mary Maloney's motivations in paragraphs 47 and 48 of "Lamb to the Slaughter"?

I believe these are the two paragraphs in question.  

It was extraordinary, now, how clear her mind became all of a sudden. She began thinking very fast. As the wife of a detective, she knew quite well what the penalty would be. That was fine. It made no difference to her. In fact, it would be a relief. On the other hand, what about the child? What were the laws about murderers with unborn children? Did they kill then both-mother and child? Or did they wait until the tenth month? What did they do?

Mary Maloney didn’t know. And she certainly wasn’t prepared to take a chance.

Mary Maloney's motivation is her unborn child.  Mary has just hit Patrick over the head with the leg of lamb, and Patrick is lying dead on the floor.  Mary knows what will happen next in terms of police, detectives, and an investigation, because Patrick is a law enforcement officer.  Mary also has a fairly good idea of what her own personal punishment will be.  She is unsure of what will happen with her baby.  Mary is currently six months pregnant, and she is unsure if she would be jailed and sentenced while pregnant.  Mary isn't willing to find out, and her motherly instinct takes over.  That's her motivation.  She is protecting her child, and she is willing to get away with murder to do it. 

Why does Mary Maloney insist the police eat the lamb in "Lamb to the Slaughter"?

Mary's husband, Patrick, announced that he was leaving her (or a divorce).  For a few minutes after that, Mary is operating on autopilot.  She moves about the house in a daze, and she decides that she is still going to cook dinner.  Mary gets the lamb, and she announces her intentions to Patrick.  He, very callously, announces that he doesn't want any dinner, because he is going out. 

"I've already told you," he said. "Don't make supper for me. I'm going out."

Mary snaps.  She hits Patrick over the head with the leg of lamb.  The blow kills him.  

Mary admits that she knows what the punishment will likely be for her, but she doesn't know what will happen to her unborn child.  She isn't willing to risk finding out, so she makes a plan to get away with the murder.  

It was extraordinary, now, how clear her mind became all of a sudden. She began thinking very fast. As the wife of a detective, she knew what the punishment would be. It made no difference to her. In fact, it would be a relief. On the other hand, what about the baby? What were the laws about murderers with unborn children? Did they kill them both -- mother and child? Did they wait until the baby was born? What did they do? Mary Maloney didn't know and she wasn't prepared to take a chance.

In order to do that, Mary needs two things.  First, she needs an alibi.  She does that by going to the grocery store and speaking to the clerk.  Second, she needs to get rid of the murder weapon.  Mary does this by cooking it and making sure the police eat all of it.  Without a murder weapon, the police have no physical evidence to tie Mary to the murder. 

Why did Mary make supper in "Lamb to the Slaughter"?

In "Lamb to the Slaughter" by Roald Dahl, Mary originally assumes she and Patrick, her husband, will have a drink and relax at home before going out to supper, as that is what they normally do on Thursdays. 

When Patrick gets home, though, he tells Mary something that upsets her a lot (it is never explicitly stated, but it is heavily implied that he tells her he wants a divorce). Mary doesn't seem to grasp this fully immediately, and insists on making supper for them at the house. She goes to the freezer and selects a leg of lamb. Patrick tells her he is going out for supper and does not want her to prepare anything for him, though, and Mary hits him in the head with the lamb, which kills him.

After she realizes what she has done, Mary decides to go to the store to get all the food she would need to make a full supper for she and Patrick. At the store, she tells the grocer that she needs to purchase vegetables because her husband surprised her by wanting to stay in for supper instead of go out that night, even though they usually always eat out on Thursdays. When Mary gets home, she proceeds to prepare the food, including the lamb. All of these actions help set it up so that Mary has an alibi when she calls the police about Patrick's death. The police believe Mary when she tells them she returned from the store to find Patrick dead, and even unknowingly help Mary get rid of the murder evidence by eating the lamb she cooked.